Clement challenges Dalton to a five kilometer car race. Dalton drives at a constant speed of 22 kilometers per hour throughout the race.

Clement waits for precisely three seconds after Dalton has reached 600 meters from the start line, and then Clement starts his car, covering every xth kilometer at the rate of 2.5*3^x kilometers per hour.

For example, Clement covers the first kilometer at the rate of 7.5 kilometers per hour , the second kilometer at the rate of 22.5 kilometers per hour and so on.

Who is the winner of the race?

This problem is solved by determining who can complete their particular distance in the shortest time. 

For Clement, that distance is 5000 m.  For Dalton, it is [5000 - 600 - 3*(22000/3600)] = 4381.667 meters.  Dalton can complete this distance in 717 seconds.

Clement divides his race into 5 1000-meter stages.  His velocity for each stage is as follows:

v1 =   2.08 m/s
v2 =   6.25 m/s
v3 =  18.75 m/s
v4 =  56.25 m/s
v5 = 168.75 m/s

Dividing distance by velocity, the times for each stage are:

t1 = 480.00 s
t2 = 160.00 s
t3 =  53.33 s
t4 =  17.78 s
t5 =   5.93 s

t-total = 717.037 seconds

Dalton wins the race by 0.037 s.

Posted by hoodat on 2007-05-02 13:16:55