In this lesson, we will learn how to solve algebra word problems that involve motion.
Related Topics: More Algebra Word Problems
d = rt
where d = distance, r = rate and t = 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 3 mph and 4 mph respectively. In how many hours will they meet?
Solution:
Let x = time walked.
r 
t 
d 

John 
3 
x 
3x 
Philip 
4 
x 
4x 
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 15mile trip 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 
4x + x 
15 / 5x 
15 
up river 
4x  x 
15 / 3x 
15 
The rate of the current is 2 mph.
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