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Ratio Problem

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Ratio Problem

by yuvarajait » Sun Apr 03, 2011 6:09 pm
It takes the average dryer 80 minutes to dry one full load of Bob's laundry. Bob has
one average dryer, and also decides to try one "Super Jumbo-Iron Dryer-Matic",
which is faster than the average dryer by a ratio of 5 : 4. Bob has three loads of
laundry, and both machines are so precise that he can set them to the minute. How
many minutes does it take for him to dry his three loads? (Assume that no time
passes between loads and that he can use both machines concurrently.Bob is allowed to switch partially-dried loads between dryers)

Could you please help deriving the answer. Thanks!
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by vineeshp » Sun Apr 03, 2011 7:26 pm
Hey.

As per the question. The Average Drier A takes 80 mins and the Super dryer is faster by 5:4. If something is faster by 5:4, it means it takes lesser time in the ratio of 4:5. (Because the load under consideration is the same, faster dryer means lesser time taken)

So the S dryer takes 80 * 4/5 = 64 minutes to finish one load.

Working together the amount of drying completed in one minute = 1/64 + 1/80
(5 + 4) / 320 = 9/320 load.
So one full load is completed in 320/9 minutes.

Time to complete 3 loads will three times : 3 * 320/9
=320/3 minutes. 106 2/3 minutes. ~ 107 minutes.

Ask me if you have any doubts.
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by manpsingh87 » Sun Apr 03, 2011 8:41 pm
vineeshp wrote:Hey.

As per the question. The Average Drier A takes 80 mins and the Super dryer is faster by 5:4. If something is faster by 5:4, it means it takes lesser time in the ratio of 4:5. (Because the load under consideration is the same, faster dryer means lesser time taken)

So the S dryer takes 80 * 4/5 = 64 minutes to finish one load.

Working together the amount of drying completed in one minute = 1/64 + 1/80
(5 + 4) / 320 = 9/320 load.
So one full load is completed in 320/9 minutes.

Time to complete 3 loads will three times : 3 * 320/9
=320/3 minutes. 106 2/3 minutes. ~ 107 minutes.

Ask me if you have any doubts.
agreed with vineesh...!! same reasoning...!!!
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by Geva@EconomistGMAT » Mon Apr 04, 2011 1:13 am
GMAT Vs. Real life :)

If you reduce this problem to GMAT methodology, 107 minutes makes sense. The problem is that assuming a rate of 9/320 means that the two driers are working together, ALL the time - which is not the case. In fact, what happens is this:

Bob will fill two loads: one slow load that will take 80 minutes, and a faster load of 64 minutes.

After 64 minutes pass, the first load is ready, and the faster drier will take the third load. This load will take 64 more minutes to dry, for a total of 128 minutes, and there's nothing you can do to shorten that time: the slow drier will finish after 80 minutes, and will just sit there waiting for the faster drier to finish.
So the answer is 128 minutes (two cycles of the faster drier), unless the problem's logic can be extended to include faster drying times for partial loads: If the machines work faster with a smaller load, then it makes sense for Bob to stop the second cycle of the fast dryer and drop a certain portion of the load in the slow drier, so that both machines are utilized for the entire time. Then we could go into the mathematics to optimize that load distribution between the two driers to minimze overall time - it's not even certain that dividing the loads half an half is the best way to go either.

Obviously, this is not a real GMAT question.
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