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*3x 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?
I converted all my speeds from km/hr to meters/second for ease.
Clement challenges <st1:City><st1:place>Dalton</st1:place></st1:City> to a 5000m car race. <st1:City><st1:place>Dalton</st1:place></st1:City> drives at a constant speed of 55/9 m/sec throughout the race.
<o:p> </o:p>
Time for Dalton = 5000m * 9/55 sec/m = 9000/11 sec = 818.181818…sec
Time for Dalton to cover 600m = 600 * 9/55 sec/m = 1080/11 sec
Clement waits for precisely three seconds after <st1:City><st1:place>Dalton</st1:place></st1:City> has reached 600 meters from the start line, and then Clement starts his car, covering every xth kilometer at the rate of 25*3x/36 m/sec.<o:p></o:p>
<o:p> </o:p>
Clement has the following speeds:
km #1 at 7.5 km/hr = 7500m/3600sec = 25/12 m/sec,
km #2 at 22.5 km/hr = 22500m/3600sec = 75/12 m/sec, km #3 at 67.5 km/hr = 67500m/3600sec = 225/12 m/sec,
km #4 at 202.5 km/hr = 202500m/3600sec = 675/12 m/sec, km #5 at 607.5 km/hr = 607500m/3600sec = 2025/12 m/sec
Time for Clement for km #1 = 1000m * 12/25 sec/m = 40*12 sec = 480 sec
Time for Clement for km #2 = 1000m * 12/75 sec/m = 40*12/3 sec = 160 sec
Time for Clement for km #3 = 1000m * 12/225 sec/m = 40*12/9 sec = 160/3 sec
Time for Clement for km #4 = 1000m * 12/675 sec/m = 40*12/27 sec = 160/9 sec
Time for Clement for km #5 = 1000m * 12/2025 sec/m = 40*12/81 sec = 160/27 sec
Time for <st1:City><st1:place>Dalton</st1:place></st1:City> to cover 600m = 1080/11 sec
Time to wait after = 3 sec
Total time for Clement = 3 + 480 + 160 + 160/3 + 160/9 + 160/27 + 1080/11 sec
= 891/297 + 142,560/297 + 47,250/297 + 15,840/297 + 5280/297 + 1760/297 + 29160/297 sec
= 242741/297 sec = 817.309764309… sec
So...I have Clement winning by roughly .872 sec.
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Posted by Mike C
on 2007-05-02 15:23:22 |
Solution - different answer
