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# Velocity and perimeter

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1. The rectangular swimming pool measures 20 feet by 70 feet and contains a path of uniform width around the four edges. The perimeter of the rectangle formed by the pool and the surrounding path is 204 feet. Determine the width of the path.

2. Use the formula :Time traveled = DISTANCE TRAVELED
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Average Velocity

A passenger train can travel 240 miles in the same amount of time it takes a freight train to travel 160 miles . If the average velocity of the freight train is 15 miles per hour slower than the average velocity of the passenger train , find the average velocity of each.

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Word Problems
Please show all steps in solving these problems. Thank you

1. The rectangular swimming pool measures 20 feet by 70 feet and contains a path of uniform width around the four edges . The perimeter of the rectangle formed by the pool and the surrounding path is 204 feet. Determine the width of the path.

The red rectangle is the swing pool which is 70 by 20 ft.
The width of the path is x ft.
Then the outside rectangle has length (70 + 2x) ft and width (20 + 2x) ft.
The perimeter of the outside rectangle is then
P = 2 * length + 2 * width
P = 2(70 + 2x) + 2(20 + 2x)
P = 140 + 4x + 40 + 4x
P = 180 + 8x
180 + 8x = 204
8x = 24
x = 24 / 8
x = 3
so the path is 3 ft wide.

2. Use the formula :Time traveled = DISTANCE TRAVELED
__________________
Average Velocity

A passenger train can travel 240 miles in the same amount of time it takes a freight train to travel 160 miles . If the average velocity of the freight train is 15 miles per hour slower than the average velocity of the passenger train , find the average velocity of each.
Let x mph be the velocity of the passenger train. Then the average velocity of the freight train is (x - 15) mph.
For the passenger train, it takes t = 240 /x hours to travel 240 miles.
For the freight train, it takes t = 160 / (x - 15) hours to travel 160 miles.
Therefore, we have the following equation:

Then
3x - 45 = 2x
3x - 2x = 45
x = 45
The average speed of the passenger train is 45 miles per hour.
x - 15 = 45 - 15 = 30 mph
the average speed of the freight train is 30 miles per hour.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com October 2, 2022, 3:44 pm ad1c9bdddf>
https://brainmass.com/physics/relative-velocity/velocity-perimeter-185351