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problem solving: rates

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by parulmahajan89 » Tue Sep 17, 2013 6:28 pm
Steve gets on the elevator on 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time,Joyce gets on a elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates,at which floor will their paths cross?

a. 19
b. 28
c. 30
d. 32
e. 44

I would like to get fastest solution to this problem. Also would this be considered as hard question?

Thanks
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by theCodeToGMAT » Tue Sep 17, 2013 7:13 pm
Is the Answer C [30]

Steps I executed:

Time to meet = DistanceGap/CombinedSpeed [since they both are moving towards each other, the speeds will be added]

Time = 40/120 = 1/3 minutes

For Steve, 1 minutes = 57 floors
1/3 minutes = 57/3 = 19 floors
hence, 11+19 = 30th Floor



Also, for Joyce
1 minute = 63 floors
1/3 minute = 63/3 = 21 floors
hence, 51-21= 30th Floor

Time taken to solve this question = 40 seconds.. So.. you can say it's one of the fastest solution :)

Can't consider this questions as hard...
parulmahajan89 wrote:Steve gets on the elevator on 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time,Joyce gets on a elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates,at which floor will their paths cross?

a. 19
b. 28
c. 30
d. 32
e. 44

I would like to get fastest solution to this problem. Also would this be considered as hard question?

Thanks
Parul
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by GMATGuruNY » Tue Sep 17, 2013 8:23 pm
parulmahajan89 wrote:Steve gets on the elevator on 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time,Joyce gets on a elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates,at which floor will their paths cross?

a. 19
b. 28
c. 30
d. 32
e. 44
Since Steve travels UP from the 11th floor, while Joyce travels DOWN from the 51st floor, the number of floors between Steve and Joyce = 51-11 = 40.

Steve's rate : Joyce's rate = 57:63 = 19:21.
The sum of the parts of this ratio = 19+21 = 40.
Implication:
When Steve and Joyce travel toward each other, of every 40 floors traveled, 19 floors will be traveled by Steve, while 21 floors will be traveled by Joyce.

Since there are a total of 40 floors between Steve and Joyce, Steve travels a total of 19 floors, while Joyce travels a total of 21 floors.
Since Steve travels up 19 floors from the 11th floor, the floor at which the two meet = 11+19 = 30.

The correct answer is C.
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