Distance Problems Practice Problems (page 2)
Distance Practice Problems
To review distance problems, go to Distance Problems Help
Set 1: Distance, Rate, and Time
- 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?
- 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?
- 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.
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.
- 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?
- 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?
- 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?
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.
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.
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.
- 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?
- 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?
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.
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.
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.
- 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?
- 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?
- 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?
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.
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.
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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