(a)
To calculate: Total distance required to run around the track.
(a)
Answer to Problem 13P
Around the track,
Explanation of Solution
Given information:
Distance to stay from inner edge of the track is 0.5 m.
Total distance required to run includes distance around left and right semicircle as well as straight line distance on the bottom and top of the track.
Since the distance to run from the inner edge is 0.5 m, the left and right semicircles have the same radius of
Thereby,
Two semicircles can be combined to make a full
Thus,
The distance around the semicircles:
Now,
The width of soccer field is 2r .
And
The length of soccer field is twice the width.
Then
The length of soccer field is 4r .
Thereby,
The straight lines on top and bottom of the track are both 4r .
Thus,
The distance around these parts of the track is 8r .
Therefore,
Around the track,
(b)
To calculate: Farther distance run by the friend.
(b)
Answer to Problem 13P
Friend runs
Explanation of Solution
Given information:
Friend stays 0.5 m from the outer edge of the track.
We know that
Width of the track is 4 m.
If friend runs 0.5 m from the outer edge, he is running 3.5 m from the inner edge.
Then
Friend is running on a semicircle with radius of
Thus,
The distance around the semicircles that friend runs:
Since the distance from the inner edge doesn’t affect the length, the straight line distances on top and bottom of the track is same for the friend.
Thus,
The straight line distance for the friend is also 8r .
Therefore,
For friend,
Now,
To know the farther distance that your friend runs than you do, subtract your distance from the distance your friend runs:
Chapter 4 Solutions
Algebra: Structure And Method, Book 1
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