SOLUTION: An automobile race is arranged between two drivers - Steady Eddy - living up to his reputation - manages to average exactly 150 kilometers per hour(kph) for the entire length of th

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: An automobile race is arranged between two drivers - Steady Eddy - living up to his reputation - manages to average exactly 150 kilometers per hour(kph) for the entire length of th      Log On


   

Question 96962: An automobile race is arranged between two drivers - Steady Eddy - living up to his reputation - manages to average exactly 150 kilometers per hour(kph) for the entire length of the race. Rapid Robert has some mechanical problems early in the race and averages 140 kph for the first half of the length of the race. Rapid Robert recovers during the later stages of the race and averages 160 kph for the second half of the length of the race. What is the outcome of the race?
Answer by mathslover(157) About Me  (Show Source):
You can put this solution on YOUR website!
let the total distance by 2d
hence time taken by Eddy 2d/150
=d/75
Time taken by Robert is d/160 + d/140
= 300d/160*140
=3d/224
to compare which of the times is larger
we rewrite the fraction d/75 as 3d/225 (multiplying the numerator and denominator by 3)
so time taken by Eddy is 3d/225
time taken by Robert is 3d/224
clearly
3d/225 < 3d/224 Since denominator is larger in the fraction
Hence Eddy is the winner