Ratios

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Ratios

by adthedaddy » Sat Sep 01, 2012 10:11 am
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. Assume also
that he never runs a machine with less than a full load. Finally, assume that Bob
is allowed to partially dry a load
in one machine and then switch it to the other.)

This is from MGMAT Word Translations Guide. The problem is solved for Bob not allowed to partially dry a load.
My question is, if Bob partially dries a load then how can it be solved. I am not able to understand the MGMAT soln.
Plz help.

Ans: 107 mins (approx)
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by aravinch » Sat Sep 01, 2012 10:24 am
Average dryer=80 minutes for one load.

Super jumbo dryer is faster than average dryer and 5:4 is tha ratio of times taken to dry using avg dryer and super jumbo dryer respectively.

ratios: 5:4

5x=80 is the time taken to dry one load avg dryer x=16

4*16 =64 minutes taken by super jumbo dryer


combinely by avg and super jumbo dryers for one load 1/80+ 1/64=80*64/80+64

for 3 loads=3*(80*64/144) =aprrox 107 minues.

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by vk_vinayak » Sat Sep 01, 2012 10:38 am
Here is a laborious way:

Time taken by avg drier = 80 min
Time taken by jumbo drier: Time taken by avg drier = 4:5 => jumbo drier takes 64 minutes.

1 load in avg drier and 1 load in jumbo drier: jumbo drier finishes in 64 minutes, and 3rd load is put into jumbo drier

In total 80 minutes, avg drier finishes 1 load, and jumbo drier finishes 1 load + some part of the 3rd load.

If jumbo drier takes 64 minutes to finish 1 load, then it will finish 1/4 load in 16 minutes.

So, at the end of 80 minutes, 2 loads are finished and 1/4 of the 3rd load is finished.

Balance amount: 3/4 of the third load. We need to divide it in 5:4 => It becomes 5/12 and 4/12.

We put 5/12 in jumbo drier and 4/12 in avg drier. Calculating either time will helps us.

If jumbo drier finishes 1 load in 64 minutes, it finishes 5/12 of load in 26.6 minutes.

Therefore total time taken is 80+26.6 ~ 107 minutes.
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