
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 25th, 2018, 12:07 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 310 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: 19,542 Thanks: 1751 
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: 13,129 Thanks: 914 
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. 

Tags 
finish, race, time 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Hangglider and racing car's race. Time of catching up  sf7  Algebra  4  April 12th, 2014 07:13 AM 
how to finish my solution?  dennisdixon  Algebra  3  March 27th, 2013 05:24 PM 
Can't finish DiffEQ  Singularity  Applied Math  2  July 25th, 2010 07:56 AM 
How to finish solving?  BMWPower06  Algebra  3  May 30th, 2008 04:46 AM 
Need help to finish my homework  ArmiAldi  Calculus  2  May 3rd, 2008 05:09 PM 