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Motion (Distance) FormulaMotion problems are based on the formula

d = rt

whered

= distance,r

= rate andt

= time.

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

Example:

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

Solution:

Let x = time walked.

r t d

John 3 x 3 x

Philip 4 x 4 x

3 x + 4 x = 147 x = 14

x = 2

They will meet in 2 hours .

Example:

In still water, Peters boat goes 4 times as fast as the current in the river. He takes a 15-miletrip up the river and returns in 4 hours. Find the rate of the current.

Solution:

Let x = rate of the current.

r t d

down river 4 x + x 15 / 5 x 15up river 4 x - x 15 / 3 x 15

The rate of the current is 2 mph .

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