Jese Hernandez-Mendoza and Eddie Martinez appeal from a judgment of conviction for one count of conspiracy to distribute methamphetamine, one count of possession with intent to distribute methamphetamine, and one count of possession with intent to distribute cocaine. The district court ^[1] denied the appellants’ motions for judgment of acquittal and sentenced each to 121 months’ imprisonment and five years of supervised release. We affirm.

I.

On February 29, 2008, Hernandez-Mendoza and Martinez were traveling east on Interstate 90 through Wyoming when Wyoming Highway Patrol Trooper Tim Boumeister stopped their vehicle for speeding. After Boumeister issued a warning citation to Hernandez-Mendoza, the driver, the trooper obtained Hernandez-Mendoza’s consent to ask additional questions and search the vehicle. Boumeister also called Captain Jeffrey Hodge, a deputy sheriff with the Crook County, Wyoming, Sheriffs Office to request his assistance in performing a canine sniff of the vehicle.

Hodge arrived on the scene and obtained consent from Hernandez-Mendoza for a drug dog to enter the vehicle. The dog alerted to the presence of drugs in the area near the dashboard. Boumeister and[*974] Hodge then searched the vehicle on the roadside for approximately one hour, but found no drugs. Law enforcement officers then took the vehicle to a Wyoming Highway Patrol garage for further examination. Approximately three hours after the initial stop, having located no drugs hidden in the vehicle, a Wyoming Highway Patrol Lieutenant concluded that there were no drugs to be found, and ordered the vehicle released.

Hodge disagreed with the Lieutenant’s decision and contacted South Dakota Highway Patrol Trooper Brian Swets. Hodge described the vehicle and told Swets that the drug dog had alerted to the vehicle. He also cited several factors about the vehicle that led Hodge to believe that the travelers were involved in illegal activity. Hodge notified Swets that the vehicle was heading east on Interstate 90 toward South Dakota.

Swets later spotted the appellants’ vehicle and stopped it for speeding. During the stop, Swets deployed his drug dog, and the dog alerted between the front and rear passenger side doors. Swets then began to search the vehicle. In the rear hatchback area, he noticed non-factory carpet, a shallow storage compartment, and loose trim. After removing the trim, Swets was able to shine his flashlight through holes in the storage compartment, and he saw several food storage containers hidden below the metal floor of the compartment. Law enforcement officers seized the containers and found methamphetamine and cocaine therein.

Trooper Nicholas Allen then arrived on the scene to transport the appellants to the South Dakota Highway Patrol Office. Unbeknownst to the appellants, Allen’s video recorder was recording the entire time they were in Allen’s vehicle. At one point, Allen left the vehicle, and the equipment recorded a conversation in Spanish between Hernandez-Mendoza and Martinez.

Once the appellants arrived at the patrol office, Agent Chad Evans of the South Dakota Division of Criminal Investigation administered to Martinez the warnings based on Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966), obtained a waiver of rights, and questioned Martinez. Martinez made incriminating statements.

After the grand jury returned an indictment, both appellants moved to suppress physical evidence seized as a result of Trooper Swets’s search and statements recorded in Trooper Allen’s vehicle. Martinez also moved to suppress his statements to Agent Evans. After a hearing, a magistrate judge recommended that the physical evidence found in the appellants’ vehicle should be suppressed, but that the recorded conversation in the back of Trooper Allen’s vehicle and Martinez’s statements to Agent Evans should be admissible. On de novo review, the district court rejected the recommendation to suppress the physical evidence, and denied the relevant portions of the motions to suppress.

A jury found the appellants guilty on all three counts of the indictment. As relevant to this appeal, the district court overruled appellants’ objection to a final jury instruction on deliberate ignorance. The court also denied the appellants’ motions for judgment of acquittal, ruling that the evidence was sufficient to support the verdicts.

II.

Appellants argue that the district court erred in denying their motions to suppress physical evidence obtained as the result of Trooper Swets’s search of the vehicle. Martinez also contends that the district court erred in denying his motion to sup[*975] press the conversation recorded in the back of Trooper Allen’s car and his statements to Agent Evans. We review the district court’s factual findings for clear error, and we review de novo the district court’s legal conclusions on a motion to suppress. United States v. McGlothen, 556 F.3d 698, 701 (8th Cir.2009).

A.

Appellants first contend that although the South Dakota traffic stop for speeding was lawful at its inception, the seizure later became unreasonable, in violation of the Fourth Amendment, because Trooper Swets did not have reasonable suspicion to investigate drug trafficking activity. A lawful traffic stop “can become unlawful if it is prolonged beyond the time reasonably required to complete” the mission of the stop. Illinois v. Caballes, 543 U.S. 405, 407, 125 S.Ct. 834, 160 L.Ed.2d 842 (2005). Appellants argue that this seizure was unreasonably prolonged.

After a valid traffic stop, an “officer may detain the offending motorist while the officer completes a number of routine but somewhat time-consuming tasks related to the traffic violation.” United States v. $404,905.00 in U.S. Currency, 182 F.3d 643, 647 (8th Cir.1999). If an officer develops reasonable suspicion of the existence of other criminal activity during the stop, then “the officer may expand the scope of the encounter to address that suspicion.” United States v. Peralez, 526 F.3d 1115, 1120 (8th Cir.2008). If an officer develops probable cause that contraband may be found in the vehicle, then it is reasonable for the officer to search the vehicle without a warrant. United States v. Donnelly, 475 F.3d 946, 954 (8th Cir.2007).

We conclude that Trooper Swets did not violate the Fourth Amendment rights of the appellants by extending the traffic stop to search the vehicle, because he had probable cause to believe there was contraband in the vehicle. But for the Wyoming traffic stop earlier in the day, this would be a simple case. Swets was accompanied at the scene by a drug dog, and his deployment of the dog to sniff the exterior of the vehicle, only six minutes into the encounter, did not impermissibly expand the scope of the traffic stop. See Caballes, 543 U.S. at 409, 125 S.Ct. 834; United States v. Rivera, 570 F.3d 1009, 1014 (8th Cir.2009). If the traffic stop by Swets had been the first encounter between appellants and law enforcement on that day, then there would be no doubt that the dog’s alert established sufficient probable cause to justify a search for contraband in the vehicle. Rivera, 570 F.3d at 1012.

Appellants contend, however, that the information from which Trooper Swets discerned probable cause is the same information that prompted the fruitless search of their vehicle in Wyoming. They argue that Swets’s dog alert simply replicated the dog alert in Wyoming, and that Swets’s other information was conveyed to him by Captain Hodge in Wyoming based on the investigation at the earlier traffic stop. Appellants urge that when officers searched the vehicle for nearly three hours in Wyoming without finding drugs, the probable cause to search dissipated, such that Swets could not renew the search based on essentially identical information. See United States v. Watts, 7 F.3d 122, 126 (8th Cir.1993) (“[A]n investigative stop must cease once reasonable suspicion or probable cause dissipates.”).

The government responds that Trooper Swets developed new information that established probable cause independent of the information gathered in Wyoming, but we deem it unnecessary to resolve that point. Even if we accept that Swets acted based in part on pre-existing probable[*976] cause developed in Wyoming, the search was not unreasonable.

The stop by Trooper Swets was based on a traffic violation, so we need not be concerned with whether the probable cause from Wyoming would justify a second seizure. Cf. United States v. Garcia, 23 F.3d 1331, 1334-35 & n. 2 (8th Cir.1994); United States v. Peters, 10 F.3d 1517, 1522-23 (10th Cir.1993). The seizure here was reasonable, and we must consider whether Swets had probable cause to search despite the previous investigation. That a law enforcement supervisor in Wyoming determined to cease searching and to release the vehicle is not dispositive, for whether probable cause exists is a question of law to be determined objectively. See Whren v. United States, 517 U.S. 806, 812-13, 116 S.Ct. 1769, 135 L.Ed.2d 89 (1996). The Wyoming lieutenant decided that the vehicle did not contain drugs; Captain Hodge disagreed. The lieutenant outranked Hodge, but law enforcement’s pecking order does not make the supervisor’s subjective opinion controlling under the Fourth Amendment. In South Dakota, Trooper Swets observed the hidden compartment and food storage containers after about ten minutes of searching the vehicle. If there had been probable cause to search for another ten minutes in Wyoming before the vehicle was released, then there was probable cause for Swets to search for ten minutes in South Dakota based on the same pre-existing probable cause.

It is well established, and well known, that drug traffickers have developed sophisticated means to secrete contraband in vehicles. See United States v. Olivera-Mendez, 484 F.3d 505, 508, 512 (8th Cir.2007); The French Connection (20th Century Fox 1971). “If probable cause justifies the search of a lawfully stopped vehicle, it justifies the search of every part of the vehicle and its contents that may conceal the object of the search.” United States v. Ross, 456 U.S. 798, 825, 102 S.Ct. 2157, 72 L.Ed.2d 572 (1982). Probable cause to search a vehicle does not dissipate simply because it takes a long time to complete a reasonable and thorough search. Olivera-Mendez, 484 F.3d at 512. It took police six hours to find a hidden compartment containing cocaine in Olivera-Mendez, and that search was reasonable. Id. at 512-13. Here, the officers in Wyoming searched for fewer than three hours and gave up. Their search did not uncover the area under the non-factory carpet and below the storage compartment in the rear of the vehicle, where Swets eventually discovered the contraband. If the Wyoming lieutenant had been more persistent, and authorized Hodge to continue searching for another ten minutes, we see no basis to conclude that a search of this carpeted area would have been impermissible. Likewise, for Trooper Swets to search areas in the vehicle that could conceal contraband, and that had not been exhausted during the discontinued investigation in Wyoming, was not unreasonable.

B.

Martinez also appeals the district court’s denial of his motion to suppress statements that he made during a recorded conversation with Hernandez-Mendoza in Trooper Allen’s car, as well as statements to Agent Evans, which he contends were fruit of an allegedly poisonous tree. Martinez argues that Allen’s activation of the recording device was the functional equivalent of custodial interrogation, and that his statements should be suppressed, because Allen did not administer Miranda warnings before the conversation was recorded. Interrogation occurs when a law enforcement officer engages in “either express questioning or its functional equivalent,” which includes “any words or actions[*977] on the part of the police (other than those normally attendant to arrest and custody) that the police should know are reasonably likely to elicit an incriminating response from the suspect.” Rhode Island v. Innis, 446 U.S. 291, 300-01, 100 S.Ct. 1682, 64 L.Ed.2d 297 (1980) (footnote omitted). “Voluntary statements not in response to an interrogation,” however, “are admissible with or without Miranda warnings.” McGlothen, 556 F.3d at 701.

Trooper Allen’s act of leaving the appellants alone in his vehicle, with a recording device activated, was not the functional equivalent of express questioning. Allen may have expected that the two men would talk to each other if left alone, but an expectation of voluntary statements does not amount to deliberate elicitation of an incriminating response. “Officers do not interrogate a suspect simply by hoping that he will incriminate himself.” Arizona v. Mauro, 481 U.S. 520, 529, 107 S.Ct. 1931, 95 L.Ed.2d 458 (1987). Allen did not question the suspects or engage in psychological ploys of the sort characterized as interrogation by the Supreme Court in Innis. See 446 U.S. at 299, 100 S.Ct. 1682. He had legitimate security reasons for recording the sights and sounds within his vehicle, see Mauro, 481 U.S. at 528, 107 S.Ct. 1931, and the appellants had no reasonable expectation of privacy in a marked patrol car, which is “owned and operated by the state for the express purpose of ferreting out crime.” United States v. Clark, 22 F.3d 799, 801 (8th Cir.1994). The requirements of Miranda, including warnings before custodial interrogation, “were designed to vest a suspect in custody with an added measure of protection against coercive police practices.” Innis, 446 U.S. at 301, 100 S.Ct. 1682. From the perspective of the appellants, we see nothing so coercive about the trooper’s simple act of leaving them alone in the patrol car that would justify characterizing Allen’s behavior as interrogation. The district court properly declined to suppress the recorded statements and the subsequent admissions to Agent Evans.

III.

Both appellants argue that the district court erred in denying their motions for judgment of acquittal. We review the district court’s decision de novo, and we reverse only if no reasonable jury could have found proof of guilt beyond a reasonable doubt. United States v. Rush-Richardson, 574 F.3d 906, 909 (8th Cir.2009). Appellants assert that the evidence was insufficient to establish the knowledge elements of the charged offenses—i.e., that they knowingly entered into an agreement to distribute narcotics, and that they knowingly possessed cocaine and methamphetamine.

We agree with the district court that the circumstantial evidence was sufficient to support the jury’s findings of knowledge. The vehicle in which the appellants were traveling contained drugs with a street value of at least $80,000, and it is reasonable to infer that a third party was unlikely to entrust a vehicle with such valuable merchandise to unwitting couriers. Law enforcement located four cell phones in the vehicle, and the government presented testimony that drug traffickers typically carry multiple cell phones to allow for the disposal of one or more, if necessary to avoid detection. There were two screwdrivers in plain view in the vehicle (one flat head and one Phillips), and Trooper Swets was able to access the hidden compartment using those tools. There was a tube of epoxy in the glove box, near the warning citation issued to Hernandez-Mendoza in Wyoming, and the screws that fastened the hidden compartment were inserted with epoxy.

There were good reasons for the jury to reject the exculpatory explanation offered[*978] by the appellants after the traffic stop. Although supposedly visiting Hernandez-Mendoza’s aunt in Fairfield, Iowa, for a week, the appellants were traveling with only one small duffle bag, and written driving directions found in the glove box did not correspond to an aunt in Fairfield.

The appellants also made statements that the jury was entitled to use to infer knowledge. In the recorded conversation in Trooper Allen’s car, the appellants appeared to express no shock or outrage upon learning that illegal drugs were found in the vehicle. When the two men were first left alone in the vehicle, one remarked that “they purchased that car at an auction; that’s all, they purchased it at an auction.” Immediately thereafter, the two engaged in this brief colloquy:

MV# 5: And, what is your aunt’s name?

MV# 4: Mh, which one?

MV# 5: The one we were going to, the one we were going to go and see.

MV# 5: Carolina.

(Exh. 7, at 3). ^[2] The jury reasonably could interpret these statements as an effort by the appellants to develop an exculpatory explanation for how drugs came to be located in the car without their knowledge, and an innocent explanation for their travel. One of the appellants later said to the other that “[w]e should have stayed back there and sleep [sic], and then drive during the night,” a statement that a jury could take to mean that nighttime travel with narcotics was more likely to avoid detection. (Ex. 7, at 4).

When asked about marijuana, cocaine, and heroin, Martinez audibly answered, looked at Trooper Swets, and shook his head no, but when Swets asked about methamphetamine, Martinez looked down and away from the trooper, and shook his head no. Similarly, Hernandez-Mendoza gave a relaxed negative answer to questions about marijuana and cocaine asked by Trooper Boumeister, but he became tense and declined to look at the trooper when denying knowledge of methamphetamine. A jury reasonably could infer that these responses indicated consciousness of guilt by the appellants about carrying methamphetamine.

We are not convinced that the decisions in United States v. Mendoza-Larios, 416 F.3d 872 (8th Cir.2005), United States v. Fitz, 317 F.3d 878 (8th Cir.2003), and United States v. Pace, 922 F.2d 451 (8th Cir.1990), require reversal. Each of these decisions is fact-intensive, and subtle differences in evidence are sufficient to justify a different outcome. In Mendoza-Larios, for example, this court held that there was insufficient evidence to prove knowledge of a hidden compartment, but the defendants in that case did not have tools necessary to access and conceal the hidden compartment, nor were the statements of the defendants as probative of knowledge as are the admissions and inconsistencies in this case. In Pace and Fitz, one or more occupants of the seized vehicle admitted knowledge of the drugs, and this court held there was insufficient evidence to establish that another occupant was also privy to the drug trafficking. Here, Hernandez-Mendoza and Martinez both denied knowledge of the contraband, and they suggest a reasonable jury could believe only that a third party left $80,000 in illegal drugs unattended with the appellants. The district court properly distinguished these precedents, and we affirm the decision to deny the motions for judgment of acquittal.

IV.

Finally, Hernandez-Mendoza argues that the district court erred by in[*979] structing the jury on “deliberate ignorance.” The district court issued this instruction:

You may find that a defendant acted knowingly if you find beyond a reasonable doubt that the defendant was aware of a high probability that he was in possession of a controlled substance and that he deliberately avoided learning the truth. The element of knowledge may be inferred if a defendant deliberately closed his eyes to what would otherwise have been obvious. You may not find a defendant acted “knowingly” if you find he was merely negligent, careless, or mistaken as to whether drugs were contained in the vehicle in which he was traveling.

(Final Instructions to the Jury, R. Doc. 128, at 18). We review a district court’s decision to give a jury instruction for abuse of discretion, United States v. Lewis, 557 F.3d 601, 613 (8th Cir.2009), and an error in the instructions may be harmless if the government establishes that it did not substantially influence the verdict. See United States v. Raether, 82 F.3d 192, 194 (8th Cir.1996).

A deliberate ignorance instruction is appropriate when the evidence is sufficient to support a jury’s conclusion that “the defendants had either actual knowledge of the illegal activity or deliberately failed to inquire about it before taking action to support the activity.” United States v. Whitehill, 532 F.3d 746, 751 (8th Cir.2008). Defendants act with deliberate ignorance if they “were presented with facts putting them on notice criminal activity was particularly likely and yet intentionally failed to investigate.” Id. A deliberate ignorance instruction should not be given, however, “[i]f the evidence in a case points solely to either actual knowledge or no knowledge of the facts in question.” United States v. Hiland, 909 F.2d 1114, 1130 (8th Cir.1990). When reviewing whether the evidence was sufficient to support a deliberate ignorance instruction, we consider “the evidence and any reasonable inference from that evidence in the light most favorable to the government.” Id. at 1131.

We have doubt about whether the instruction was properly given in this case. The government asserts that the deliberate ignorance instruction was appropriate because if it is assumed that the appellants lacked actual knowledge of the drugs, several pieces of information — a drug dog alert in Wyoming and modifications to the interior of the vehicle — put them on notice of likely criminal activity before they traveled to South Dakota. The difficulty with holding the appellants accountable for failing to inquire into these suspicious facts, however, is that the appellants also knew that law enforcement in Wyoming had undertaken a fruitless search for drugs. Could it reasonably be said that appellants “failed to investigate” a suspicion of illegal drugs in the vehicle when they consented to allow law enforcement officers to conduct a three-hour search of the vehicle? The government also contends that the appellants should have been on notice of illegal drugs in the vehicle, because their luggage was not consistent with their purported travel plans. This contention seems to confuse deliberate ignorance with actual knowledge; appellants’ suspicious story and meager luggage was evidence of the latter but not the former.

Nonetheless, we conclude that any error in giving the deliberate indifference instruction was harmless. There was sufficient evidence to convict appellants based on actual knowledge of the illegal drugs, and we assume that the jury relied on that theory, rather than an unlikely theory of deliberate ignorance. As the Supreme Court explained in Griffin v. United States, 502 U.S. 46, 59-60, 112 S.Ct. 466,[*980] 116 L.Ed.2d 371 (1991), jurors are well equipped, based on their own intelligence and expertise, to analyze the evidence, so there is reason to think that a jury would rely on a factually adequate theory rather than a factually inadequate one. The government’s theory that appellants actually knew of the illegal drugs was factually adequate. We are confident that any error in charging the jury on the alternate theory of deliberate ignorance did not substantially influence the verdict.

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The judgment of the district court is affirmed.