Algebra Motion Problems



In this lesson, we will learn how to solve algebra word problems that involve motion.

Related Topics: More Algebra Word Problems

Motion (Distance) Formula

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 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 15-mile 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.

Videos

Motion Word Problems
Students should first draw a diagram to represent the relationship between the distances involved in the problem, then set up a chart based on the formula rate times time = distance. The chart is then used to set up the equation.

Two cars leave from the same place at the same time and travel in opposite direction. One car travels at 55 mph and the other at 75 mph. After how many hours will there be 520 mph apart?



Motion Problem - involving speed, distance and time.
John left his house at 3.00 pm to drive 60 mph to drive towards Michigan. Phoebe left the same house at 5.00 pm, driving 80 mph in the same direction as John. How long will it take Phoebe to overtake John?






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?



Problem: Gordon rode his bike at 15 mph to get his car. He then drove back at 45 mph. If the entire trip took him 8 hours, how far away was his car?






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?







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