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# Distance Problems Practice Problems (page 2)

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By McGraw-Hill Professional
Updated on Sep 26, 2011

#### Solutions

1. The distance between the girls is decreasing at the rate of 8 + 7 = 15 mph. Let t represent the number of hours they are on their bicycles.

15 t = 5

The girls will meet in of an hour or 20 minutes.

2. The distance between the cars is decreasing at the rate of 65 + 55 = 120 mph. Let t represent the number of hours the cars have traveled since entering the highway.

120 t = 270

The cars will meet after hours or 2 hours 15 minutes.

3. The distance between the joggers is decreasing at the rate of 6 + 9 = 15 mph. Let t represent the number of the hours they are jogging.

15 t = 9

The joggers will meet after of an hour or minutes.

### Set 4: Traveling at Right Angles

To review distance problems involving the complication of two bodies traveling at right angles, go to Distance Problems Help.

#### Practice

1. Two joggers start jogging on a trail. One jogger heads north at the rate of 7 mph. Eight minutes later, the other jogger begins at the same point and heads south at the rate of 9 mph. When will they be two miles apart?
2. Two boats head toward each other from opposite ends of a lake, which is six miles wide. One boat left at 2:05 going 12 mph. The other boat left at 2:09 at a rate of 14 mph. What time will they meet?
3. The Smiths leave the Tulsa city limits, heading toward Dallas, at 6:05 driving 55 mph. The Hewitts leave Dallas and drive to Tulsa at 6:17, driving 65 mph. If Dallas and Tulsa are 257 miles apart, when will they pass each other?

#### Solutions

1. The first jogger had jogged miles when the other jogger began. So there is miles left to cover. The distance between them is growing at a rate of 7 + 9 = 16 mph. Let t represent the number of hours the second jogger jogs.

In of an hour, or minutes after the second jogger began, the joggers will be two miles apart.

2. The first boat got a mile head start. When the second boat leaves, there remains miles between them. When the second boat leaves the distance between them is decreasing at a rate of 12 + 14 = 26 mph. Let t represent the number of hours the second boat travels.

In hour, or minutes, after the second boat leaves, the boats will meet. That is, at 2:29 both boats will meet.

3. The Smiths have driven miles outside of Tulsa by the time the Hewitts have left Dallas. So, when the Hewitts leave Dallas, there are 257 – 11 = 246 miles between the Smiths and Hewitts. When the Hewitts leave Dallas, the distance between them is decreasing at the rate of 55 + 65 = 120 mph. Let t represent the number of hours after the Hewitts have left Dallas.

hours, or 2 hours 3 minutes , after the Hewitts leave Dallas, the Smiths and Hewitts will pass each other. In other words, at 8:20, the Smiths and Hewitts will pass each other.

### Set 5: Three Unknowns

To review distance problems with three unknowns, go to Distance Problems Help.

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