SOLUTION: Two long distance runners start from the same point on a quarter-mile oval track. Alex runs at a constant speed of exacly 10.98MPH, and Kelly runs at a constant speed of exacly 10.

Question 1130711: Two long distance runners start from the same point on a quarter-mile oval track. Alex runs at a constant speed of exacly 10.98MPH, and Kelly runs at a constant speed of exacly 10.65MPH. How many feet will they be away from the starting point when Alex laps Kelly the SECOND time.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
A hint at starting this:
How much time is the difference between their distances, two of a quarter of a mile? Time passed is what when their distances differ by half-mile?
Answer by ikleyn(52782) (Show Source): You can put this solution on YOUR website!
.

The condition did not say that they started simultaneously and ran in one direction, but I will assume that it is so.

Alex will laps Kelly first time at the moment, when Alex covers the distance, which exactly one quarter mile (precisely the length of the track) longer than the distance Kelly covers to this moment. ===--->>> It is the key point to understand when solving such problems (!) <<<---=== This condition takes the form of THIS equation 10.98*t - 10.65*t = 0.25, or (10.98 - 10.65)*t = 0.25, 0.33*t = 0.25 t = = 0.757576 of an hour. At that time moment Kelly will cover 10.65*0.757576 = 8.068 miles. So, Kelly will complete 8*4 = 32 full quarter-mile track lengths and will be at 0.068 miles from the starting point on the track. To find the moment of the SECOND lap, we can formally determine the time when Alex will overtake/lap Kelly in two track lengths. It leads to the similar equation, but you can complete the solution even without using equation. Simply note that the position of the first lap now plays the role of the former starting point. As soon as you understand it, you will guess the ANSWER: ===--->>> the second lap point is remoted 2*0.068 = 0.136 miles from the starting point. <<<---===

Solved.

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My answer 0.136 of a mile means 0.136 of a mile counting in the same direction on the track as they run.

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