Algebra Motion Problems
Step 1: Draw a diagram to represent the relationship between the distances involved in the problem.
Step 2: Set up a chart based on the formula: rate × time = distance.
Step 3: Use the chart to set up one or more equations.
Step 4: Solve the equations.
We will look at three types of Motion Word Problems:
1. Two objects going in opposite directions.
2. Both objects going in the same direction, but one goes further.
3. One object going and returning at different rates.
Solve Motion Word Problems: Two objects going in opposite directions
Example: 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 miles apart?
Related Topics: More Algebra Word Problems
What are Motion or Distance Word Problems?
Motion problems are based on the formula
d = rt
where d = distance, r = rate and t= time.
How to solve Motion or Distance Word Problems?Step 1: Draw a diagram to represent the relationship between the distances involved in the problem.
Step 2: Set up a chart based on the formula: rate × time = distance.
Step 3: Use the chart to set up one or more equations.
Step 4: Solve the equations.
We will look at three types of Motion Word Problems:
1. Two objects going in opposite directions.
2. Both objects going in the same direction, but one goes further.
3. One object going and returning at different rates.
Solve Motion Word Problems: Two objects going in opposite directions
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. After 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: 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 miles apart?
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