Relative rates .. similar approach different answers

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Car A and car B travel around a circular park with a radius of 20 miles. Both cars leaves from the same point. Car A travels counter-clockwise at 60 miles per hour and car B travels clockwise at 40 miles per hour. Car B leaves 20 minutes after car A. Approximately how many minutes does it tak for the cars to meet after car A starts?

A. 63
B. 75
C. 83
D. 126
E. 188


My problem is that answers coming differently if I adopt different methods. What am I doing wrong ?

Solution A:

Total distance to be covered by both cars approx = 2 x 3.14 x 20 = 125.6 miles

Since car A has already left 20 mint ago - it has already travelled = 20 miles

The distance now remained to be covered by both cars is approx = 106 miles

Car B now starts after 20 mints

(Relative Rates) x T = total dist to be covered

100T = 100.6
T=1.06 .. approx 63 mints

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Solution B:

Distance by Car A + Distance by Car B = Total Distance
60T + 40(T-20/60) = 125.6
100T - 40/3 = 125.6
T = 1.39
approx = 83 minutes

Correct answer is 83 and not 63 mintes - whats the difference b/w two solutions. I got this wrong since I used Solution A.

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by prindaroy » Mon Jul 27, 2009 1:34 pm
You forgot to complete solution A which is why you got it wrong. It's 63 minutes plus 20 minutes = 83 minutes, since B started 20 minutes later.

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by prindaroy » Mon Jul 27, 2009 1:36 pm
You forgot to complete solution A which is why you got it wrong. It's 63 minutes plus 20 minutes = 83 minutes, since B started 20 minutes later.

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by California4jx » Mon Jul 27, 2009 1:38 pm
ah - thanks !