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Speed and Distance, Expert please reply

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by mayank.arora » Fri Jul 15, 2011 10:16 am
Simon and Tim start a race at the same time. Simon completes each lap around the racetrack at an average speed of 60mph, and Tim at an average speed of 65mph. How many laps will Simon complete before Tim is a whole lap ahead of him?

A) 20
B) 13
C) 12
D) 10
E) 6
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by sandeeptalla450 » Fri Jul 15, 2011 10:59 am
Assume each lap is 'x' miles long.
Time taken by Simon to complete 1 lap = x/60
Distance covered by Tim in this time = (x/60)*65= 13x/12

So, Tim is ahead of Simon by a distance = (13x/12) - x = x/12 ; which means that which each lap that Simon covers Tim will be ahead of him by 1/12th of a lap. So, after 2 laps Tim will be ahead of Simon by 2*(1/12)=1/6th of a lap.

So, after 12 laps, Tim will ahead of Simon by one complete lap.
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