How to Solve Travel Problems on the ASVAB

You will see travel problems on the ASVAB. Travel problems involve using the distance formula, d = rt, where d is the distance, r is the rate, and t is the time. Generally, the problems come in three basic flavors: traveling away from each other, traveling in the same direction, and traveling at 90-degree angles.

Traveling away from each other

When two planes (or trains, cars, people, or even bugs) travel in opposite directions, they increase the distance between them in direct proportion. To solve these types of problems, you compute the distance traveled from the starting point for each plane (or train, car, person, or bug).

Train A travels north at 60 mph. Train B travels south at 70 mph. If both trains leave the station at the same time, how far apart will they be at the end of two hours?

To solve this problem, you compute the distance traveled by train A and then the distance traveled by train B and add the results together.

The distance formula is d = rt. The rate of travel for train A is 60 mph, and it travels for two hours:

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Train A travels 120 miles during the two-hour period.

When using the distance formula, you have to pay attention to the units of measurement. Remember the apples-and-oranges rule. If rate (r) is expressed in kilometers per hour, your result (d) will be kilometers. If rate (r) is expressed as miles per second, you must either convert it to mph or convert time (t) to seconds.

The rate of travel for train B is 70 mph, and it also travels for two hours:

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Train B travels 140 miles during the two-hour period.

Train A is 120 miles from the station and train B is 140 miles from the station, in the opposite direction. The two trains are 120 + 140 = 260 miles apart.

Traveling in the same direction

If two trains are traveling in the same direction as each other but at different rates of speed, one train travels farther in the same time than the other travels. The distance between the two trains is the difference between the distance traveled by train A and the distance traveled by train B.

Train A travels north at 60 mph. Train B also travels north, on a parallel track, at 70 mph. If both trains leave the station at the same time, how far apart will they be at the end of two hours?

Train A traveled 120 miles, and train B traveled 140 miles. Because they’re traveling in the same direction, you subtract to find the distance between them: 140 – 120 = 20. The two trains are 20 miles apart.

Traveling at 90-degree angles

Some travel problems involve two people or things moving at 90-degree angles and then stopping; the problem then asks you what the distance is (as the crow flies) between the two people or things, which means you need to use the distance formula and a little basic geometry.

Train A travels north at 60 mph. Train B travels east at 70 mph. Both trains travel for two hours. Then a bee flies from train A and lands on train B. Assuming the bee flew in a straight line, how far did the bee travel between the two trains?

Train A travels 120 miles, and Train B travels a distance of 140 miles.

Because the trains are traveling at 90-degree angles (one north and one east), the lines of travel form two sides of a right triangle.

The Pythagorean theorem says that if you know the length of two sides of a right triangle, you can find the length of the third side by using the formula a2 + b2 = c2:

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The bee flies 184.39 miles.

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Finding the square root of a very large number can be a daunting task, especially because you don’t have a calculator available during the ASVAB. When you reach this point of the equation, just squaring the possible answers to see which one works is often easier.

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