Answer :
22 because 7 minutes per mile in 11 miles would be 77 minutes, and 5 minutes per mile in 11 miles would be 55 minutes. Therefore it takes Luke 22 more minutes than it takes Colleen to run the mile.
Speed of a object is defined as the total distance covered in the total time taken. To run 11 miles Luke take 22 minutes longer than the colleen to run 11 miles.
Given information-
Luke can run a mile in 7 minutes.
Colleen can run a mile in 5 minutes.
What is speed?
Speed of a object is defined as the total distance covered in the total time taken. Speed is the ratio of the distance [tex]d[/tex] to the time taken [tex]t[/tex]. Thus,
[tex]s=\dfrac{d}{t}[/tex]
As Luke can run 1 mile in 7 minutes. Thus the speed of the Luke is,
[tex]s_l=\dfrac{1}{7}[/tex]
Thus the speed of the Luke is 1/7 miles per minute.
As Colleen can run 1 mile in 5 minutes. Thus the speed of the Colleen is,
[tex]s_c=\dfrac{1}{5}[/tex]
Thus the speed of the Luke is 1/5 miles per minute.
The total time taken by the Luke to cover the 11 miles with the speed of 1/7 miles per minute is,
[tex]\dfrac{1}{7} =\dfrac{11}{t}[/tex]
Solve for [tex]t[/tex]
[tex]t=11\times 7}\\t=77[/tex]
Hence, the total time taken by Luke to run 11 miles is 77 minutes.
The total time taken by the Colleen to cover the 11 miles with the speed of 1/5 miles per minute is,
[tex]\dfrac{1}{5} =\dfrac{11}{t}[/tex]
Solve for [tex]t[/tex]
[tex]t=11\times 5}\\t=55[/tex]
Hence, the total time taken by Colleen to run 11 miles is 55 minutes.
Extra time taken by Luke to cover 11 miles than Colleen is,
[tex]t=77-55=22[/tex]
Hence to run 11 miles Luke take 22 minutes longer than the colleen to run 11 miles.
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