Algebra Motion Problems

Motion problems are based on the formula

d = rt

where d = distance, r = rate and t = time.

When solving motion problems, a sketch is often helpful and a table an be used for organizing information.

Example:

John and Philip who live 14 miles apart start at noon to walk toward each other at rates of 3 mph and 4 mph respectively. In how many hours will they meet?

Solution:

Let x = time walked.

3x + 4x = 14
7x = 14
x = 2

They will meet in 2 hours.

Example:

In still water, Peter’s boat goes 4 times as fast as the current in the river. He takes a 15-mile trip up the river and returns in 4 hours. Find the rate of the current.

Solution:

Let x = rate of the current.

The rate of the current is 2 mph.

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