ASVAB distance, rate and time problems
Every distance problem on the ASVAB uses one formula: distance equals rate times time (d = rt). The harder versions add a twist: two travelers, a head start, a round trip or a current. Set up a small table with rate, time and distance for each traveler and the twist becomes simple arithmetic.
What formula do you use for ASVAB distance problems?
Use d = r × t. If you know two of the three values, you can find the third: rate is distance divided by time, and time is distance divided by rate. These questions belong to Arithmetic Reasoning, which the official site describes as the "ability to solve arithmetic word problems" (What to Expect).
Example: A convoy drives 195 miles in 3 hours. What is its average speed?
- Rate = distance ÷ time.
- 195 ÷ 3: 180 ÷ 3 = 60 and 15 ÷ 3 = 5, so 65.
Answer: 65 miles per hour
For every problem with more than one traveler, draw this grid and fill it in before you calculate:
| Traveler | Rate | Time | Distance |
|---|---|---|---|
| A | ? | ? | rate × time |
| B | ? | ? | rate × time |
| Link | add or subtract rates | same or offset times | total or equal distances |
How do you handle minutes and hours?
Turn minutes into hours before you use a speed in miles per hour. Divide minutes by 60, or use the fractions below, which come up often enough to memorize.
| Minutes | Fraction of an hour | Decimal |
|---|---|---|
| 6 | 1/10 | 0.1 |
| 10 | 1/6 | about 0.167 |
| 12 | 1/5 | 0.2 |
| 15 | 1/4 | 0.25 |
| 20 | 1/3 | about 0.333 |
| 30 | 1/2 | 0.5 |
| 40 | 2/3 | about 0.667 |
| 45 | 3/4 | 0.75 |
| 50 | 5/6 | about 0.833 |
Example: How many minutes does it take to drive 18 miles at 45 miles per hour?
- Time = 18 ÷ 45 hours.
- Simplify: 18/45 = 2/5 hour.
- 2/5 of 60 minutes = 24 minutes.
Answer: 24 minutes
A time like 2 hours 15 minutes is 2.25 hours, not 2.15 hours. Writing 2.15 is one of the most common slips on rate questions.
How do you solve problems where two vehicles move apart or toward each other?
When two travelers move in opposite directions, or head toward each other, add their speeds. The gap between them changes at the combined rate.
Example: Two trucks leave the same depot at the same time in opposite directions, one at 55 mph and one at 65 mph. When will they be 360 miles apart?
- The gap grows at 55 + 65 = 120 miles per hour.
- Time = 360 ÷ 120 = 3.
- Check: 55 × 3 = 165 and 65 × 3 = 195. 165 + 195 = 360.
Answer: 3 hours
The same addition works for trains starting at two cities and heading toward each other: their combined speed closes the distance between the cities.
How do you solve catch-up problems?
When one traveler chases another in the same direction, subtract the speeds. First find the head start distance, then divide it by the difference in speed.
Example: A truck leaves a base at 40 mph. One hour later a car leaves the same base on the same road at 60 mph. How long after the car leaves does it catch the truck?
- Head start: in 1 hour the truck covers 40 × 1 = 40 miles.
- The car gains 60 − 40 = 20 miles every hour.
- Time to close 40 miles: 40 ÷ 20 = 2 hours.
- Check: car drives 60 × 2 = 120 miles. Truck drives 40 × 3 = 120 miles. Same spot.
Answer: 2 hours after the car leaves
Read carefully whether the question asks for time after the second traveler leaves or total time since the first one left. Those answers differ by the head start, and both often appear in the choices.
How do you find average speed for a round trip?
Divide total distance by total time. Averaging the two speeds gives the wrong answer whenever you spend different amounts of time at each speed, which is almost always.
Example: You drive 120 miles to a training site at 60 mph and return the same 120 miles at 40 mph. What is your average speed for the whole trip?
- Time out: 120 ÷ 60 = 2 hours.
- Time back: 120 ÷ 40 = 3 hours.
- Total distance 240 miles, total time 5 hours.
- Average speed = 240 ÷ 5 = 48.
Answer: 48 mph (not 50)
The answer is below the simple average because you spend more time at the slower speed. If 50 mph is one of the choices, it is there to catch people who averaged.
How do current and wind problems work?
A current or wind adds to your speed when it pushes you and subtracts when you go against it. Downstream speed is boat speed plus current, upstream speed is boat speed minus current.
Example: A boat moves 12 mph in still water. The river current is 3 mph. How long does a 45 mile trip downstream take?
- Downstream speed: 12 + 3 = 15 mph.
- Time = 45 ÷ 15 = 3.
Answer: 3 hours
Going back upstream at 12 − 3 = 9 mph would take 45 ÷ 9 = 5 hours. Planes with a tailwind or headwind follow the same rule.
How do you find arrival times and compare trips at different speeds?
Find the travel time with t = d ÷ r, then add it to the start time. When the same trip is driven at a different speed, find the distance first, then the new time.
Example: You leave at 8:30 a.m. and drive 150 miles at 60 mph. When do you arrive?
- Time = 150 ÷ 60 = 2.5 hours, which is 2 hours 30 minutes.
- Add it to 8:30: 8:30 + 2:00 = 10:30, then + 0:30 = 11:00.
Answer: 11:00 a.m.
Example: A trip takes 4 hours at 50 mph. How long does the same trip take at 40 mph?
- Distance = 50 × 4 = 200 miles.
- New time = 200 ÷ 40 = 5 hours.
- Check the direction: slower speed, so the trip must take longer.
Answer: 5 hours
Speed and time move in opposite directions for a fixed distance. If you cut the speed to 4/5 of the original, the time grows to 5/4 of the original. That inverse relationship helps you check your work: an answer that makes the trip faster at a lower speed is wrong.
How do you solve rate problems that are not about travel?
The same formula works for any rate: amount = rate × time. Replace distance with pages, gallons, parts or miles per gallon, and keep the units attached to each number so you can see what cancels.
Example: A printer prints 18 pages per minute. How long does a 450 page job take?
- Time = amount ÷ rate = 450 ÷ 18.
- 18 × 25 = 450, so the time is 25 minutes.
Answer: 25 minutes
Example: A truck drives 360 miles on 12 gallons of fuel. How far can it go on 21 gallons?
- Fuel rate: 360 ÷ 12 = 30 miles per gallon.
- Distance on 21 gallons: 21 × 30 = 630 miles.
Answer: 630 miles
When a problem gives a rate "per" something, that word marks the bottom of the fraction. Miles per gallon is miles over gallons. Pages per minute is pages over minutes. Writing the rate as a fraction tells you whether to multiply or divide: gallons × (miles over gallons) leaves miles. Many Arithmetic Reasoning items are this kind of everyday rate problem with a military or job setting, and the ratios and rates lesson has more unit rate drills.
How do you avoid mistakes on rate problems?
Most errors come from units and from answering a different question than the one asked. Before you pick an answer, run a short check:
- Are the units matched? Miles with miles per hour, minutes converted to hours.
- Did you add speeds for opposite directions and subtract for chasing?
- Does the answer make sense? A car at 60 mph cannot cover 300 miles in 2 hours.
- Did the question ask for distance, time or speed? Underline it before you start.
For more rate practice, see the ratios and rates lesson and the full list of word problem types. Timed sets are on the Arithmetic Reasoning practice page.
Practice questions
Work each one on paper first, then open the explanation. These are original AptiStep items, not real ASVAB questions.
A bus travels 270 miles at an average speed of 54 miles per hour. How long does the trip take?
- 4.5 hours
- 6 hours
- 5 hours
- 5.4 hours
Show answer and explanation
Answer: C. 5 hours
Time = distance ÷ rate = 270 ÷ 54. Since 54 × 5 = 270, the trip takes exactly 5 hours. Check by multiplying back: 54 × 5 = 270 miles.
Two trains start 420 miles apart and travel toward each other, one at 65 mph and the other at 75 mph. After how many hours do they meet?
- 3 hours
- 6 hours
- 3.5 hours
- 42 hours
Show answer and explanation
Answer: A. 3 hours
Moving toward each other, the gap closes at 65 + 75 = 140 mph. Time = 420 ÷ 140 = 3 hours. Check: 65 × 3 = 195 and 75 × 3 = 225, and 195 + 225 = 420. The 42 hour choice comes from subtracting the speeds.
You walk 2.5 miles in 50 minutes. What is your speed in miles per hour?
- 2 mph
- 3 mph
- 5 mph
- 0.05 mph
Show answer and explanation
Answer: B. 3 mph
50 minutes is 50/60 = 5/6 of an hour. Speed = 2.5 ÷ 5/6 = 2.5 × 6/5 = 15/5 = 3 mph. The 0.05 choice divides miles by minutes without converting to hours.
A driver covers 30 miles at 60 mph and then 30 more miles at 30 mph. What is the average speed for the 60 miles?
- 45 mph
- 50 mph
- 35 mph
- 40 mph
Show answer and explanation
Answer: D. 40 mph
First leg: 30 ÷ 60 = 0.5 hour. Second leg: 30 ÷ 30 = 1 hour. Total: 60 miles in 1.5 hours, and 60 ÷ 1.5 = 40 mph. Averaging 60 and 30 gives 45 mph, which ignores the extra time spent at the slower speed.
A cyclist leaves at 12 mph. Thirty minutes later a second cyclist leaves from the same spot on the same route at 18 mph. How long after the second cyclist starts does she catch up?
- 30 minutes
- 1 hour
- 1.5 hours
- 2 hours
Show answer and explanation
Answer: B. 1 hour
Head start: 12 mph × 0.5 hour = 6 miles. The second cyclist gains 18 − 12 = 6 miles per hour. Time to catch up: 6 ÷ 6 = 1 hour. Check: she rides 18 miles; the first cyclist rides 12 × 1.5 = 18 miles.
A boat goes 15 mph in still water. The current is 3 mph. How long does it take to travel 36 miles upstream?
- 2 hours
- 2.4 hours
- 4 hours
- 3 hours
Show answer and explanation
Answer: D. 3 hours
Upstream the current slows the boat: 15 − 3 = 12 mph. Time = 36 ÷ 12 = 3 hours. The 2 hour choice uses the downstream speed of 18 mph, and 2.4 hours ignores the current.
How far does a vehicle travel in 2 hours 15 minutes at 48 mph?
- 103.2 miles
- 108 miles
- 96 miles
- 120 miles
Show answer and explanation
Answer: B. 108 miles
15 minutes is 1/4 hour, so the time is 2.25 hours. Distance = 48 × 2.25 = 96 + 12 = 108 miles. The 103.2 choice treats 2 hours 15 minutes as 2.15 hours.
Frequently asked questions
Is there a shortcut for distance, rate and time?
Cover the value you want in the triangle d over r and t: what remains tells you to multiply (r × t) or divide (d ÷ r, d ÷ t). The table method on this page is more reliable for two travelers.
Why is round trip average speed not the average of the two speeds?
Because you spend more time at the slower speed. Average speed is total distance divided by total time.
Are distance problems on Arithmetic Reasoning or Mathematics Knowledge?
They are word problems, so they belong to Arithmetic Reasoning, the "ability to solve arithmetic word problems" (official ASVAB).
Sources
Checked November 14, 2026. AptiStep is an independent study site; confirm anything that affects your enlistment with a recruiter.