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.
Motion Word Problems
This is how to set up motion problems for Algebra.
Three Types of Problems
1. Both going the same direction but one going further
2. Two going in opposite directions
3. Going in one direction and then returning at a different rate.
Problem:
Two planes leave the same point at 8 AM. Plane 1 heads East at 600 mph and Plane 2 heads West at 450 mph. How long will they be 1400 miles apart? At what time will they be 1400 miles apart? How far has each plane traveled?
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.