In these lessons, we will learn how to solve algebra word problems that involve motion.

Related Topics:

More Algebra Word Problems

**What are Motion or Distance Word Problems?**

Motion problems are based on the formula**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**

**How to solve motion word problems with objects traveling in opposite directions?**

**Solve Motion Word Problems: Two objects going in the same direction**

**How to solve motion word problems with objects traveling in the same direction?**

**Solve Motion Word Problems: One object going and returning at different rates**

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.

Related Topics:

More Algebra Word Problems

Motion problems are based on the formula

d = rt

where d = distance, r = rate and t = time.

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.

** 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: **

** Example: **

** Example: **

** Example: **

**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.

** Example: **

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.

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