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# Distance Problems Practice Problems

based on 1 rating
By McGraw-Hill Professional
Updated on Sep 26, 2011

## Distance Practice Problems

To review distance problems, go to Distance Problems Help

### Set 1: Distance, Rate, and Time

#### Practice

1. Lori starts jogging from a certain point and runs 5 mph. Jeffrey jogs from the same point 15 minutes later at a rate of 8 mph. How long will it take Jeffrey to catch up to Lori?
2. A truck driving east at 50 mph passes a certain mile marker. A motorcyclist also driving east passes that same mile marker 45 minutes later. If the motorcyclist is driving 65 mph, how long will it take for the motorcyclist to pass the truck?

#### Solutions

1. Lori has jogged

miles before Jeffrey began. Jeffrey is catching up to Lori at the rate of 8 – 5 = 3 mph. How long will it take a body traveling 3 mph to cover miles?

Let t represent the number of hours Jeffrey jogs.

Jeffrey will catch up to Lori in hours or minutes.

2. The truck traveled miles. The motorcyclist is catching up to the truck at a rate of 65 – 50 = 15 mph. How long will it take a body moving at a rate of 15 mph to cover miles?

Let t represent the number of hours the motorcyclist has been driving since passing the mile marker.

The motorcyclist will overtake the truck in hours or 2 hours 30 minutes.

### Set 2: Traveling in Opposite Directions

To review distance problems when two bodies are moving in opposite directions, go to Distance Problems Help.

#### Practice

1. Two airplanes leave an airport simultaneously, one heading east; the other, west. The eastbound plane travels at 140 mph and the westbound plane travels at 160 mph. How long will it take for the planes to be 750 miles apart?
2. Mary began walking home from school, heading south at a rate of 4 mph. Sharon left school at the same time heading north at 6 mph. How long will it take for them to be 3 miles apart?
3. Two freight trains pass each other on parallel tracks. One train is traveling west, going 40 mph. The other is traveling east, going 60 mph. When will the trains be 325 miles apart?

#### Solutions

1. The planes are moving apart at a rate of 140 + 160 = 300 mph. Let t represent the number of hours the planes are flying.

In hours, or 2 hours 30 minutes, the planes will be 750 miles apart.

2. The distance between the girls is increasing at the rate of 4 + 6 = 10 mph. Let t represent the number of hours the girls are walking.

Mary and Sharon will be 3 miles apart in of an hour or minutes.

3. The distance between the trains is increasing at the rate of 40 + 60 = 100 mph. Let t represent the number of hours the trains travel after leaving the station.

The trains will be 325 miles apart after hours or 3 hours 15 minutes.

### Set 3: Traveling Towards Each Other

To review distance problems when two bodies travel toward each other, go to Distance Problems Help.

#### Practice

1. Jessie leaves her house on a bicycle, traveling at 8 mph. She is going to her friend Kerrie’s house. Coincidentally, Kerrie leaves her house at the same time and rides her bicycle at 7 mph to Jessie’s house. If they live 5 miles apart, how long will it take for the girls to meet?
2. Two cars 270 miles apart enter an interstate highway traveling towards one another. One car travels at 65 mph and the other at 55 mph. When will they meet?At one end of town, a jogger jogs southward at the rate of 6 mph. At the opposite end of town, at the same time, another jogger heads northward at the rate of 9 mph. If the joggers are 9 miles apart, how long will it take for them to meet?

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