Michael and Ben decide to run a 100m race. While training for the race Michael's best time was 13.5s and Ben's best time was 15.0s. How far behind should Michael start so that the race end in a tie? Assume that Ben and Michael will run at top speed.

11.05 m

Explanation:

Given:

Total distance = 100 m

Time taken by Michael = 13.5 s

Time taken by Ben = 15 s

Thus,

Speed of Michael = Distance / Time = 100 / 13.5 = 7.407 m/s

Speed of Ben = Distance / time = 100 / 15 = 6.67 m/s

Now,

let Micheal is 'x' m far behind the Ben

thus,

total distance covered by Michael to complete the race = (x + 100) m

now for equal time to complete the race by both

also, time = Distance / Speed

thus,

Time taken by Michael = Time taken by Ben

or

(100 + x) / 7.407 = 100 / 6.67

or

x = 11.05 m