# Motion Problem Solving

Noya drives into the city to buy a software program at a computer store. Because of traffic conditions, she averages only 15 mi/h. If the total travel time is 2 hours, how long does it take her to drive to the computer store?

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Try it risk-free Visualize two different roadways; one is an interstate with cars traveling at 70 mph, and the other is a main street going through a town with traffic lights every 200 feet.

On which road do you think you would find uniform motion?

For example, if the problem asks you how long it will take for Person/Entity 2 to catch and overtake Person/Entity 1 In other words, Person/Entity 1 would in theory have to travel an additional 2 miles in order for his distance to equal Person/Entity 2’s distance.

This will all make more sense once you see how this strategy is applied to a sample GMAT question.

The same rules apply; you may just need to apply them more than once to solve a problem. You need to individually determine the time for each driver, then determine the time of arrival based on information given in the problem. Once you know two, you can solve for the third using algebraic rules.

Remember to use logic as you consider the problem and always to return to the actual problem when you are ready to state your solution so that your solution is given in terms of the problem. Complex problems sometimes require multiple steps, but the steps always follow the same logic.

Uniform motion problems may involve objects going the same direction, opposite directions, or round trips. A high-speed train leaves the same station an hour later. The second train follows the same route as the first train on a track parallel to the first.

In the diagram below, the two vehicles are traveling the same direction at different rates. Since the distances are equal, the products of rate and time for the two cars are equal. A table can also help you understand relationships in distance-rate-time problems. In how many hours will the second train catch up with the first train?

Barring traffic accidents, cars would be expected to constantly travel at 70 mph.

On the other hand, the street going through the town has traffic lights that are designed to stop traffic.

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