A tank of volume 432 cubic feet has one inlet pipe and 2 out

Question

A tank of volume 432 cubic feet has one inlet pipe and 2 outlet pipes. The inlet pipe fills water into the tank at the rate of 4 cubic inches/min and the 2 outlet pipes empty it out at the rates of 14 cubic inches/min and 6 cubic inches/min respectively. If all 3 pipes are opened when the tank is full in how much time is it emptied?(1 foot = 12 inches)

A. 777.6 hrs
B. 3 days
C. 15 days
D. 77.76 hrs
E. 5 days

Show Answer

Official Answer

A

A. 777.6 hrs
B. 3 days
C. 15 days
D. 77.76 hrs
E. 5 days

shalva · Answer

I think the main difficulty here is to calculate the answer.

So every minute 4 cubic inches of water are poured in the tank, 20 cubic inches - out

Every minute water volume diminishes by exactly 20-4=16 cubic inches. How fast would the tank become emptied?

Volume of the tank = 432 cubic feet (not inches) = 432 *12 *12 *12 cubic inches. We should divide volume by drainage rate:

(432*12*12*12)/16 = 46,656 minutes = 777.6 hours = 32.4 days

The main problem is to perform this last calculation within reasonable time. Personally, I couldn't do it in 2 minutes

prome2 · Answer

Edit: (after format)
432/16 * 1728/60 (simplify) - I did it in 2 mins 5 secs

1 foot = 12 inches
(1 foot)^3 = (12 inches)^3
1 foot^3 = 1728 inches^3

---------

432 * 1728 cubic inches = capacity of tank

Time in hours to empty tank = 432 * 1728
 ------------
 60 * (14+6-4)
 
 = 432 * 1728
 ---- -----
 16 60
 
 = 27 * 288
 ----
 10
 
 = 7776
 ----- hrs
 10

kp1811 · Answer

will go with A -777.6hrs

just hope with option A hrs is missing with 777.6

kirankp · Answer

OA is A and its 777.6 hrs

jeckll · Answer

Eek I got all the way through and realized I only multiplied 432  ft^3  by 12! When it should be 12*12*12 ... stupid mistake ... this is definitely a tough one in 2 mins

jeckll · Answer

But I am surprised there was no "trap" answer as I got 5 hours 24 minutes because I divided 5,184 cubic inches (432*12) by 16. I would have thought that trap would have been there for me to fall into!

mustafaj · Answer

Agreed, this one is time consuming. I got the same answer, is there a shortcut ? (it took me over 2 minutes

hussi9 · Answer

opps I missed the cubic part ...

nishtil · Answer

I got it well over 2 min is there any short cut for such a calculation

chawlavinu · Answer

A is definitely correct!!

For me it just took over 2 mins and few seconds. Good One.. Answer A is missing the unit hrs.

jhays · Answer

My first time through I did it the long, long way. When I did it again I decided against actually multiplying anything out and it seemed to go quicker. YMMV.

432 * 12^3 = 16t

Convert the 432 into 16 * 27

(16 * 27 * 12^3) / 16 = t

27 * 12^3 = t

Divide by 60 to convert seconds to hours

(27 * 12^3) / 60 = t

Convert one of the 12s into 2 * 6.

(27 * 2 * 6 * 12^2) / 60 = t

(27 * 2 * 12^2) / 10 = t

Multiply out 54 * 144 (much quicker than multiplying 432 * 1728) and divide by 10 for the answer: 777.6 hours.

On the other hand, given the wide range of the answer choices, what is everyone's opinion on simplifying the numbers and taking an estimate?

Also, is it reasonable to assume that the correct answer must be an exact answer because the question stem doesn't specifically ask for an approximate answer? If so, you could eliminate all the answers given in days once you find out that the answer in minutes isn't divisible by 60 (which is as soon as you set up the equation). If you can eliminate the "days" answer choices, the only other answer choices are an order of magnitude apart. Perfect candidates for estimation!

smthsteve6 · Answer

432 Cubic feets = 432 * 12 * 12* 12 cubic inches

tank drained per min = 14+6+4 cubic inches = 16 cubic inches
Per hour = 16* 60

rate = 432*12*12*12/16*60
 = 7776/10
 =777.6

Ans A

KarishmaB · Answer

The options are such that you don't have to calculate a whole lot.
3 days is 72 hrs (think less than 100 if you will)
15 days is 360 hrs (10 days have 240 hrs so 5 days have 120 so overall, 15 days have 360 hrs)

Look at the question now:

The tank has one inlet pipe and 2 outlet pipes. When all 3 pipes are open, think what is happening in one minute.

4  in^3  is flowing in the tank and (14+6)  in^3  is flowing out of the tank. So overall, in every one minute, 20-4 = 16  in^3  is flowing out of the tank.

Now we have the volume of the full tank. In every minute, 16  in^3  flows out of it. How long will it take to empty?

\frac{432*12*12*12 in^3}{16}  minutes

We see that 16*27 = 432 (I wondered if 432 will directly go by 16. I saw that it does. It's good to know the multiplication tables)

Let's convert it to hours now:  \frac{27*12*12*12 in^3}{60}  hours
=  \frac{27*12*12 in^3}{5}  hours

Now this is painful calculation so I will try to ballpark.

I say that 27/5 is more than 5.
I know that 12*12 = 144
So answer will be more than 5 times 144 which has to be option (A).

jlgdr · Answer

Actually till here (432*12*12*12)/1 its same thing as I did. Then I quickly looked at answer choices to see what units was the answer expressed in Then decided to divide by 60 as well. Got 144*27 / 5 Approximated to 144*5 = 720 A little more than that Only A made sense Hope it helps Cheers! J

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A tank of volume 432 cubic feet has one inlet pipe and 2 out

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