In these lessons, 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.
Aaron left L.A. to drive at 55 mph towards Las Vegas. Mike left L.A. an hour after Aaron (also towards Las Vegas), driving at 70 mph. How long will it take Mike to overtake Aaron?