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August 25th, 2018, 12:07 AM   #1
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how much time does A finish the race?

A and B are racing at a 1 km track. A gives B a start of 100m and beats him by 15 seconds. A in his over confidence, gives B a start of 90 seconds, but loses by 500 m. In how much time does A finish the race?

Answer is 120 sec.
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August 25th, 2018, 08:16 AM   #2
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If A runs 1 km in t seconds, the details of the first race imply that B needs (t + 15) seconds to run (900/1000)km, and the details of the second race imply that B needs ((500/1000)t + 90) seconds to run 1 km.

As (t + 15) = (9/10)(t/2 + 90) implies t = ((9/10)90 - 15)/(1 - (9/10)(1/2)) = 120, A needs 120 seconds to run 1 km.
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August 25th, 2018, 01:56 PM   #3
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Thanks Skip...you inspired my general case formula!

a = A's speed (?)
d = distance (1000m)
u = time by which A beats B (15)
v = distance given by A (100m)
w = distance A loses by (500m)
x = time A gives B (90)

a = [vw - d(v + w)] / [vx + d(u - x)] = 8 1/3

So time by A = d / a = 1000 / 8 1/3 = 120

Try this one Ganesh:
A and B are racing at a 1200 miles track.
At first race, A gives B a start of 360 miles and beats him by 2 hours.
At next race, A gives B a start of 12 hours, but loses by 400 miles.
In how much time did A finish the first race?
Thanks from Ganesh Ujwal

Last edited by Denis; August 25th, 2018 at 02:14 PM.
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