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August 25th, 2018, 12:07 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 476 Thanks: 1  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. 
August 25th, 2018, 08:16 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,028 Thanks: 2259 
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. 
August 25th, 2018, 01:56 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 
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? Last edited by Denis; August 25th, 2018 at 02:14 PM. 

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