Distance, rate, and time are essential concepts in the ASVAB exam. Mastering these concepts is crucial for success in the Mathematics Knowledge section. Understanding the relationship between distance, rate, and time is important for solving problems related to speed, velocity, and time taken to travel a certain distance. By practicing various problems and scenarios related to distance, rate, and time, test-takers can improve their problem-solving skills and time management during the exam. This guide will cover the basic formulas, strategies, and tips to tackle Distance, Rate, & Time questions effectively. Whether you are a beginner looking to build a strong foundation or aiming to enhance your problem-solving abilities, mastering Distance, Rate, & Time will undoubtedly boost your confidence and performance on the ASVAB exam.

ASVAB

If the average speed of an airplane is 525 miles per hour, how many miles can it travel in 6 hours?

Previously, you saw that the formula for distance is d = r × t, that is, distance = rate × time. In this case, distance = 525 × 6 = 3,150 miles.

On a trip to the beach you travel 200 miles in 300 minutes. How fast did you travel?

First convert the 300 minutes to hours by dividing by 60 (300 ÷ 60 = 5 hours). Use the distance formula (d = rt) and substitute the known values: 200 = 5r => r = 40.

If a car travels 360 kilometers in 5 hours, how many kilometers will it travel in 9 hours when driving at the same speed?

First calculate the distance the car travels in 1 hour: 360 km ÷ 5 hours = 72 km per hour Then multiply this number by the total number of hours traveled: 9 hours × 72 km per hour = 648 km.

A train headed south for Wichita left the station at the same time a train headed north for Des Moines left the same station. The train headed for Wichita traveled at 55 miles per hour. The train headed for Des Moines traveled at 70 miles per hour. How many miles apart were the trains at the end of 3 hours?

The train headed for Wichita traveled 55 miles per hour × 3 hours = 165 total miles. 
 The train headed for Des Moines traveled 70 miles per hour × 3 hours = 210 total miles. 
 Adding the distances together gives you the number of miles apart the two trains were after three hours: 210 + 165 = 375. 
 Another option: You can add the two rates of speed (55 + 70) 
 And multiply the sum by 3 hours (125 × 3 hours = 375).

A recruit reporting to boot camp took a bus from her home to the military processing center in another city. The trip took 14 hours. If she left at 6 a.m., what time did she arrive at the processing center?

Simply add 14 hours to 6 a.m. to reach 8 p.m.

A car is driven 750 miles in 25 hours. What is the rate of the car in miles per hour?

The rate of the car is 750miles/25hours. Dividing 25 into 750 gives 30, so the car is traveling at 30 miles per hour.

Light travels 744,000 miles in 4 seconds. What is its speed in miles per second?

The speed (rate) is 744,000 miles/4seconds. Dividing 4 into 744,000 gives you 186,000 miles per second.

Two bicyclists head toward each other from the opposite ends of Main Street, which is six miles long. The first biker started at 2:05 going 12 mph. The second biker began peddling 4 minutes later at a rate of 14 mph. What time will they meet?

The first bike got a @@@@@@@@@@@@@@@@@@@@ mile head start (12 × @@@@@@@@@@@@@@@@@@@@@@@). 

Therefore, by the time the second bike leaves, there are @@@@@@@@@@@@@@@@@@@@@@@ miles between them (6 – @@@@@@@@@@@@@@@@@@@@). 

Their combined rate of travel is 12 + 14 = 26 mph. 

Let t = the number of hours the second bike travels.

26t =  @@@@@@@@@@@@@@@@@@@@@@@

26t =  @@@@@@@@@@@@@@@@@@@@@@@

t =  @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

t =  @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

t =  @@@@@@@@@@@@@@@@@@@@

@@@@@@@@@@@@@@@@@@@@  of an hour = 12 minutes. The second bike left at 2:09, so both bikes will meet at 2:21.

Keith is driving from Reno to Kansas City to meet his girlfriend. The distance between the two cities is 1,650 miles. If Keith can average 50 miles per hour, how many hours will it take him to complete his trip?

1,650 miles (total distance) ÷ 50 miles per hour (average speed) = 33 hours.

How much time is there between 7:45 am today and 3:15 pm tomorrow?

From 7:45 am today to 7:45 am tomorrow is 24 hours. From 7:45 am tomorrow to 3:15 pm tomorrow is @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ hours. Add them up and we get the correct answer.

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@  hours.

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@  hours.

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ hours.

Rachel is driving to visit her mother, who lives 250 miles away. How long will the drive be, round-trip, if Rachel drives at an average speed of 40 mph?

The distance from Rachel’s house to her mother’s house is 250 miles, so round-trip, the distance is 500 miles. Plug this into the distance formula: 
 d = rt
 500 = 40t
 500 ÷ 40 = t
 12.5 = t
 It takes Rachel 12.5 hours to make the round-trip drive. Since 1 hour = 60 minutes, multiply by 60 to find the answer in minutes:
 12.5 × 60 = 750 minutes.

An aircraft flies over Boondock Air Force Base at 10:20 a.m. At 10:32 a.m, the plane passes over Sea Side Naval Air Station, 120 miles away. How fast is the aircraft traveling?

The aircraft travels 120 miles in 12 minutes, which is 1/5 of an hour. Therefore, in 55 (one) hour, it would travel 5 × 120, or 600 miles. The aircraft is traveling 600 miles per hour.

A balloonist circumnavigated the globe in 13 days, 12 hours, 16 minutes, and 13 seconds. A plane circumnavigates the globe in 4 days, 10 hours, 15 minutes, and 7 seconds. How much longer did it take for the balloon to go around the world?

Subtract the speed of the plane from the speed of the balloon to determine how much longer it took the balloonist.

8 days, 14 hours, 16 minutes, and 6 seconds.

9 days, 2 hours, 1 minute, and 6 seconds.

9 days, 7 hours, 3 minutes, and 20 seconds.

12 days, 7 hours, 11 minutes, and 35 seconds.

Your car uses gasoline at the rate of 21 miles per gallon. If gasoline costs $2.82 per gallon, and you drive for 7 hours at a speed of 48 miles per hour, how much will you pay for gasoline for the trip?

Your first step is to determine the number of miles traveled. Multiply the rate of travel by the time. 48 × 7 = 336 miles. The amount of gas used is the total miles driven, divided by the number of miles per gallon. 336 ÷ 21 = 16 gallons of gasoline used. At the price of $2.82 per gallon, you spent $45.12 for gas ($2.82 × 16 = $45.12).

ASVAB Distance, Rate, & Time: Mastering the Essentials

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ASVAB Distance, Rate, & Time: Mastering the Essentials

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