Pipe A that can fill a tank in an hour and pipe B that can fill the

Question

Pipe A that can fill a tank in an hour and pipe B that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe B is shut 15 minutes before the tank overflows. When will the tank overflow?

A) 30 mins
B) 35 mins
C) 40 mins
D) 32 mins
E) 36 mins

Source : 4gmat

A) 30 mins
B) 35 mins
C) 40 mins
D) 32 mins
E) 36 mins

Source : 4gmat

Bunuel · Accepted Answer

The last 15 minutes only pipe A was open. Since it needs 1 hour to fill the tank, then in 15 minutes it fills 1/4th of the tank, thus 3/4 of the tank is filled with both pipes open.

The combined rate of two pipes is 1 + 2 = 3 tanks/hour, therefore to fill 3/4th of the tank they need (time) = (work)/(rate) = (3/4)/3 = 1/4 hours = 15 minutes.

Total time = 15 + 15 = 30 minutes.

Answer: A.

iaratul · Answer

I think I might be able to give a more elaborate reply:

Rate for Pipe A: 1/60
Rate for Pipe B: 1/30
Working together, their rate is 1/60 + 1/30 = 1/20

Pipe A and B work together 15 minutes before Pipe B quits. So, Pipe A is practically running solo for the last 15 minutes.

Therefore, for Pipe A to work alone for the last 15 minutes:
Rate x Time = Work
1/60 x 15 = 1/4 - Means Pipe A has to fill up 1/4th of the tank alone.

Remaining capacity = 1 - 1/4 = 3/4

Now, it's obvious that Pipe A and B worked together and completed 3/4th of the task. So
Rate x Time = Work
1/20 x Time = 3/4; Time = 3/4 x 20 = 15 minutes

Result = Time taken for Pipe A and B to work together + Time taken for Pipe A to work solo = 15 minutes + 15 minutes = 30 minutes.

Temurkhon · Answer

1/60+1/30=1/20t/min working together

Let 's try backsolving:

better to start from B, i.e. 35 min. 35-15=20, that is 1/20*20=1 meaning that tank was full when pipes worked together, it contradicts condition, eliminate B,C,E

go D, i.e. 32 min. 32-15=17, that is 1/20*17=17/20 working together means 3/20 working A alone. Check, 1/60*15=15/60=1/4>3/20, so eliminate D

So, must be A

we can check 30-15=15*1/20=15/20=3/4. 15/60=1/4. It is correct

Ashishmathew01081987 · Answer

Let,
Work done by Pipe A in 1 min = 1/60
Work done by pipe B in 1 min = 1/30

Work done by both Pipe A & Pipe B in 1 min = 1/60 + 1/30 = 1/20

Pipe B is shut down for the last 15 Mins. So, the work in those fifteen minutes is done by Pipe A
= 15 * (1/60) = 1/4

Remaining 3/4th part of the work was completed by Both Pipe A & Pipe B

Setting up proportion

in 1 min Both A & B do 1/20 th part of work 
Therefore to complete 3/4th part of the work time required = 15 min

So, total time required for the tank to overflow 
= Time for which Pipe A was running alone + Time for which both Pipe A & Pipe B were running together
= 15 min + 15 min
= 30 Min

Answer A

bhaskar438 · Answer

Work= Rate * Time  
Let's say Work = 1 Task

Rate of Pipe A=  \frac{1}{60}  \frac{task}{minute}  
 Rate of Pipe B=  \frac{1}{30}  \frac{task}{minute}

Pipe B is shut down 15 minutes before Pipe A, so if Pipe B worked for  t-15 minutes , then Pipe A worked for  t minutes. 
So,   Combined work = Pipe A work + Pipe B work   -->   1 Task =  \frac{t-15}{30} + \frac{t}{60}

At this point, you can either solve the quadratic or plug in answer choices. It would be quickest to plug in answer choices. Choice  A  works.

ufo9038 · Answer

Time needs to fill tanks: x 
A runs all the time so in x hour it fills x portion of the tank.
B doesn't run the last 15 mins (=1/4 hour) so it runs (x-1/4) hour. During this time it fills 2(x - 1/4) of the tank. 
Together they fill the tank. So x + 2(x-1/4) = 1 
Solve for x we have 1/2 = 30 mins. So A.

CounterSniper · Answer

The question states B can fill the Tank when empty in 30 Minutes while A can do it in 60 Minutes.
also
B is turned off 15 minutes prior to overflow
which means B was on for 15 minutes 
now since B can fill the tank in 30 minutes , it would have filled 50% of the tank in 15 minutes while A would have filled 25% in 15 minutes
after this point only A is kept open and we know that , A can fill 25% in 15 minutes which also happens to be the remaining space left in the tank.
Thus Tank will overflow after 15 minutes. Total time taken =30 minutes

guialain · Answer

To avoid fractions and percentages - which might look scary for some of us- let work with Smart numbers.

Let asume that the tank is 60 liters. (Of course, 120 or other numbers will lead to the same result)
A fills the tank in 1 hour, A work at 1 liter per min.
B fills the tank in 30 min, B work at 2 liters per min.
A&B together work at 3 liters per min.

In the last 15 min, A works alone to complete filling the tank with the remaining 15 liters. 
Therefore, before B was shut down, A&B had worked together to fill the tank with 45 liters (60-15). This takes 15 min.

Answer is 30 min.

gracie · Answer

let t=time to fill tank
1*t+2(t-1/4)=1
t=1/2 hour=30 minutes
A

JeffTargetTestPrep · Answer

We see that the rate of pipe A = 1/1 = 1, and the rate of pipe B = 1/(½) = 2. We can let the time used to fill the tank by pipe A = n hours; thus, the time used to fill the tank by pipe B = (n - 1/4), and create the equation:

1(n) + 2(n - 1/4) = 1

n + 2n - 1/2 = 1

3n = 3/2

n = (3/2)/3 = 1/2 hour = 30 minutes.

Answer: A

anmolgmat14 · Answer

Time taken by Pipe A= 1/60
Time taken by Pipe B=1/30

Total time taken=1/20

Now B was shut 15 minutes before overflow that means together Pipe A and Pipe B worked for 5 minutes
i.e 1/4 of the work

Now for rest of 3/4 of work is done by Pipe A, which means time taken to complete 3/4th of work by pipe A alone will be 3/4*60 =45 minutes.

Isn't the total time be 50 minutes then ?

Archit3110 · Answer

rate of Pipe A ; 1/60
rate of Pipe B ; 1/30
together rate ; 1/60+1/30 ; 1/20
its clear that pipe A has to work alone in last 15 mins
so work done by A in 15 mins ; 15* 1/60 = 1/4
work done before by A &B = 3/4
1/20* time = 3/4
time = 15 mins
so total time by when tank overflows ; 15+ 15 ; 30 mins
IMO A

Prasannathawait · Answer

Let the capacity be 100
Rate of A = 100 perhour, Rate of B is 200 perhour.

Let the time to overflow be x
A operated for full X hours.
B operated for x-1/4 hours
Hence we can make an equation: Work1 + Work2 = Total Work
100x+200(x-1/4)=100
Solving this will get x=1/2 hour= 30mins.

bumpbot · Answer

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