Running a Race In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner?
Running a Race In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner?
Solution Summary: The author calculates the distance by which the second place runner beat the third place.
Running a Race In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner?
Expert Solution & Answer
To determine
To find: The distance by which the second place runner beat the third place runner.
Answer to Problem 84AYU
Solution:
10 feet
Explanation of Solution
Given:
•
• The first winner crosses the finish line 10 feet ahead of the second-place runner and 20 feet ahead of the third place runner.
Formula Used:
Calculation:
Let, be the speeds of 1st, 2nd and 3rd runners respectively.
When the first runner finishes the distance of 5280 feet in time , the second runner has covered 5270 feet and the 3rd runner has covered 5260 feet.
In time , the speeds of the three runners are
-----Eq(1)
-----Eq(2)
-----Eq(3)
Let be the time for the second runner to complete the race
-----Eq(4)
Substituting from Eq(2) in Eq(4)
-----Eq(5)
The distance travelled by third runner by the time
-----Eq(6)
Substituting Eq (3) and Eq(5) in Eq (6) we get,
The distance by which the second runner is ahead of the third runner is
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