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Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by AJWILL » Sat Aug 11, 2012 10:57 pm
Two cars started simultaneously towards each other at constant rates of 20 miles per hour and 30 miles per hour, respectively. How much time is required for these cars to cross each other, if initially they are separated by a distance of 1320 yards? (1 mile = 1760 yards)
[A] 54 sec.
51 sec.
[C] 52 sec.
[D] 53 sec.
[E] 44 sec
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by theCEO » Sun Aug 12, 2012 4:03 am
1320 yards = 0.75miles

speed x time = distance
both cars travel a total distance of 0.75miles

speed of car 1 x time + speed of car 2 x time = total distance cars travellled
20miles/hr x a + 30miles/hr x a = 0.75miles
a(20miles / hr + 30miles/hr) = 0.75miles
a(50miles/hr) = 0.75miles
a = 0.75miles/(50miles/hr) = 0.015hr
0.015hr = 0.015*60*60 = 54sec

ans = a
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by vinay911 » Wed Oct 17, 2012 12:30 am
Hi,
can we do this using relative speeds concept ? I am unable to get it right with that approach.

Please help.
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by \'manpreet singh » Wed Oct 17, 2012 7:48 pm
AJWILL wrote:Two cars started simultaneously towards each other at constant rates of 20 miles per hour and 30 miles per hour, respectively. How much time is required for these cars to cross each other, if initially they are separated by a distance of 1320 yards? (1 mile = 1760 yards)
[A] 54 sec.
51 sec.
[C] 52 sec.
[D] 53 sec.
[E] 44 sec



This kind of question can be solved by relative speed concept easily:

Since the cars are moving towards each other, we can add up their speeds= 30 + 20=50 miles/hr

Now the distance is 1320 yards, convert it in miles= 1320/1760=.75 miles

time(T) = distance/speed= .75/50 hr

T = .75/50 * 3600 sec
T= 54 sec

Hope it clears the doubt :)

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by Cosmas » Wed Nov 28, 2012 7:04 am
Let the two cars be A and B.

Car A travels at 20miles/hour
Car B travels at 30miles/hour

The distance between the cars is reducing at a rate of 50miles/hour(THE KISS:MGMAT WORD TRANSLATIONS)

Covert 50miles/hour to miles/second=1/72 miles per second.
Convert 1320 yards into miles=3/4miles.

So to get the time in seconds:

3/4miles(total distance) divided by 1/72 miles per second=54seconds.

So answer is A
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