Motion Problem Solving

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Method: variables given: r = 150 fps, t = 300 s (notice the conversion from minutes to seconds to match the rate units given). Substitute known variables and solve: d = 1.5(300) = 450 Given our solution, the bug will travel 450 feet in 5 minutes. The formula for uniform motion problems is d = rt, which means distance is equal to rate times time.

Sometimes, uniform motion problems are complex, involving more than one item in motion. Convert 1.6 hours into hours and minutes to get 1 hour and 36 minutes. Convert 1.3 hours into hours and minutes and get 1 hour and 20 minutes (rounded). You must be given two of these variables to solve a uniform motion problem.

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.

Also, remember that sometimes there will be additional steps required after your solution is found. Look for things that are the same and always look for those variables to determine what you know and what you need to find.

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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?

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