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speed problem - fastest method reqd

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by vishal.pathak » Sat Nov 19, 2011 3:49 am
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5

What is the fastest way of solving this problem
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by GMATGuruNY » Sat Nov 19, 2011 4:20 am
vishal.pathak wrote:A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5

What is the fastest way of solving this problem
2 seconds longer per 1k = 150 seconds longer per 75k.
Since there are 3600 seconds in 1 hour, the additional time needed to travel 75k at the slower rate = 150/3600 = 1/24 hours.
Since time and rate have a reciprocal relationship, 25/24 of the normal time implies 24/25 of the normal rate:
(24/25)*75 = 72.

The correct answer is B.
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by Anurag@Gurome » Sat Nov 19, 2011 7:37 pm
Solution:
The car covers 1 km at the speed of 75 km/hr.
Time taken to cover this distance is (1/75) hours = 3600/75 seconds = 144/3 = 48 seconds.
So, travelling at constant speed, time taken is 48 + 2 = 50 seconds = 50/3600 hours.
Hence, speed of car = {1/(50/3600)} km/hr = 360/5 = 72 km/hr

The correct answer is B.
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