How many hours would it take Pump A and Pump B working together, each

Question

How many hours would it take Pump A and Pump B working together, each at its own constant rate, to empty a tank that was initially full?

(1) Working alone at its constant rate,Pump A would empty the full tank in 4 hours 20 minutes.
(2) Working alone, Pump B would empty the full tank at its constant rate of 72 liters per minute.

ID: 700109
DS15349

LogicGuru1 · Accepted Answer

(1) Working alone at its constant rate,Pump A would empty the full tank in 4 hours 20 minutes.
A will empty the tank in 260 minutes. 
Rate of A * 260min= VOLUME TO BE EMPTIED
We don't know the rate of A or volume of the tank 
INSUFFICIENT

(2) Working alone,Pump B would empty the full tank at its constant rate of 72 liters per minute.
B's rate is 72 litre per minute. 
72*time = volume
We don't know volume of the tank so or how much time B takes to empty. 
INSUFFICIENT

Combining 1 and 2, we still don't know the total water in the tank 
rate of A*260 = 72*time of B
Even if we change rate into time or time into rate, we will still have two unknowns {volume and time} or {volume or rate} 
{V and R } or {V and T}

Obvious enough we still cannot solve this equation because we do not know the volume

INSUFFICIENT

ANSWER IS E

GMATBusters · Answer

absolute rate of doing work = Amount of work done per unit time .
For example: Ram writes 5 pages in an hour. Here the exact amount of work done per hour is given

rate in terms of total work: 
Suppose Ram needs to finish an assignment in 2 hours. then the rate required is 0.5 assignment per hour. This rate is in terms of total work to be done.

Now if the assignment consists of 10 pages, then both rates are equivalent. 
0.5 assignment per hour. = 5 pages in an hour.

hsbinfy · Answer

E

A)A's rate is there
B)B's rate is given in litre/min

1+2
not suff
We don't know the total time for B to empty tank

deddex · Answer

Explanation in video format by GMAT Quantum https://gmatquantum.com/official-guides ... nt-review/

gmexamtaker1 · Answer

Hello guys...

I know that this is a simple problem but I have questions.

In many work/rate problems we create the WRT table and after having the 4hrs and 20 min for (1) we assume that the total work equals 1 and we have the rate which is 1/(time of pump A to complete the work). This basically helps us determine the % of completion per hour!

In (2) we are given the actual rate which is understandable that doesn't help since we don't know the total liters or total time.

Q1: Is it wrong to say that the rate for pump A from (1) is 1/(4hrs 20mins) meaning 23% of the work per hour?
Q2: Logically since we know from (1) the rate and from (2) the rate we can find the total time by adding the two rates and find the reciprocal of the result. Why we can't do that?
Q3: If we had on (2) the time of completion the (1+2) would be SUFFICIENT? -- We could use the same logic as (1).

Please let me know. I must have missed something...

I have the exact same question , can anybody shed some light on this issue?
Why can't we approach it by setting 1/260 + 72 =1/x ?
 gmatbusters   chetan2u   Bunuel   VeritasKarishma

GMATBusters · Answer

Please find attached the response to your queries:
Q1: Is it wrong to say that the rate for pump A from (1) is 1/(4hrs 20mins) meaning 23% of the work per hour?
 It is valid.

Q2: Logically since we know from (1) the rate and from (2) the rate we can find the total time by adding the two rates and find the reciprocal of the result. Why we can't do that?
from (1), we know the  rate of A  in terms of  total work , from 2, we know the  B's absolute rate of doing work   but since, we don't know the total work, we can't find the rate of B in terms of total work and hence  can't  use them as you mentioned.

Q3: If we had on (2) the time of completion the (1+2) would be SUFFICIENT? -- We could use the same logic as (1).
 if time of completion of B given ,then we can find the rate of B in terms of total work, so using both statements 1 &2, we can find answer, hence  sufficient.

gmexamtaker1 · Answer

gmatbusters  thank you for the prompt reply, just one question could you elaborate on the difference between absolute rate of doing work and the rate in terms of total work?

CEdward · Answer

Nice C-trap problem

How many hours would it take Pump A and Pump B working together, each at its own constant rate, to empty a tank that was initially full?

(1) Working alone at its constant rate,Pump A would empty the full tank in 4 hours 20 minutes.
Insufficient b/c we don't know B.
(2) Working alone, Pump B would empty the full tank at its constant rate of 72 liters per minute.
Insufficient b/c we don't know A.

C: Careful, B doesn't actually tell us how long it would take to empty the tank, only that it does so at 72 litres / minute. We would need the actual duration as in A.

E.

ScottTargetTestPrep · Answer

Solution:

We need to determine the number of hours it takes Pump A and Pump B working together, each at its own constant rate, to empty a tank that was initially full.

Statement One Alone:

We are given the time it takes Pump A alone to empty the full tank. However, since we don’t know the time it takes Pump B alone to empty the full tank, we can’t determine the time it takes both pumps working together to empty the full tank. Statement one alone is not sufficient.

Statement Two Alone:
 
We are given the rate of Pump B. However, since we know neither the rate of Pump A nor the full capacity of the tank, we can’t determine the time it takes both pumps working together to empty the full tank. Statement two alone is not sufficient.

Statements One and Two Together:

We are given the rate of Pump B to be 72 liters per minute and we can determine the rate of Pump A to be 1/(4 x 60 + 20) = 1/260 of the tank per minute. However, since these two rates are not in the same units and we don’t know the full capacity of the tank, we can’t determine the time it takes both pumps working together to empty the full tank. Both statements together are not sufficient.

Answer: E

kumari555 · Answer

if we take single unit work like assume some fixed capacity and solve then we get answer easily. I don't understand why together we can't get answer

ManishaPrepMinds · Answer

(1)  Pump A alone can empty the tank in 4 hours 20 minutes
That’s 260 minutes ⇒ A’s rate = (1/ 260) tank/ min 
 (2)  Pump B empties the tank at 72 liters per minute
B’s rate = 72 liters/min
Problem:
 
 A's rate is in  tanks/min , B’s in  liters/min  
 We  can’t combine  the two rates unless we know the  tank volume in liters  
 So, we can’t find  total time  without converting B’s rate into tanks/min — and for that, we need the tank size.

Now, let’s test with assumed tank capacities to see what happens

If tank capacity =  720 liters 
 
 A's rate = (1/260) tank/ min  
 B's rate : 720 /72 = 10 min ⇒ (1/10) tank/ min  
 Combined rate = 1/260 + 1/10 = 27/260 tank per min 
  Total time  = 1 / (27/260) =  ~9.6 min

If tank capacity  = 7,200 liters 
 
 B’s rate : 7,200 / 72 = 100 min ⇒ (1/ 100 ) tank/ min 
 Combined rate = 1/260 + 1/100 = = 36/2600 tank per min  
  Total time  = 1 / (36/2600) =  ~72.2 min

So the time changes based on the tank’s assumed size ⇒  Cannot be determined  from given info.
Hope this is clear!

kumari555 · Answer

Thank you so much

I missed the important i.e tank/minute and other is lt/min

nikitathegreat · Answer

What do we mean by that the rate is not in the same units? So, basically A rate will be calculated considering how much they will empty in 1min considering 1 unit needs to be emptied. Whereas B rate is given where we know the volume of the tank and in 1min it is emptying 72L? SO, since the volume of tank is not known we cannot calculate the time and hence cannot inverse the time to find rate of B when it is emptying 1 unit? Hence, the answer is E?

Aboyhasnoname · Answer

This is for those who are wondering if when we solve most of the Work Rate problems with taking 1 as work and then find the answer...whats happening here that we can't find....

Remember when we take 1. We consider this a whole Job...... 
I can Build a wall in 10 hours....My rate is 1/10? Yes, but 1/10 of what?....I am building 1/10th part of wall every hour......but we don't know how much feet it is.... It can be 1 feet per hour or a 1000 feet per hour.....

Now someone is coming and building another wall, at the rate of 1 feet per hour.... but how much is 1 feet per hour? Is it 1/10th of the wall? or the whole wall? or 1/1000th part of the wall?

So it is important to remember whenever we take 1 unit of work...We consider the whole job as 1 unit.... The rate we get is in relation to the whole job... 
Filling 1/10th of a tank and 1/10 litres are not the same thing.... Unless we know that tank is of 1 litre we cannot say this. 
If we know tank is of 1 litre...Then We can say that 1/10th of tank means 1/10 litres....

So in this question...A is emptying the tank in 4 hours 20 minutes...Means 260 Minutes...Means emptying 1/260 Parts of tank in 1 minute.... 
Here 1/260 we dont know how many litres....

B is 72 litres per minute.....

Their combined rate is 1/260th part of tank + 72 litres in 1 minute...

The core in this question is not the full capacity of the tank....If the rate of B would have been in the way that rate of A was given, then we don't need full capacity ...The core is the units/Measurements/which are different and we have no relation to establish between them......

We could have got the answer if 
We would have known if 72 litres is how much part of the tank 
or instead of 72 litres B is emptying how much part of the tank 
or A doing 1/260th part of the Job translates to how many litres in a minute..... 
or the full capacity of the tank....

Hence E.

How many hours would it take Pump A and Pump B working together, each

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How many hours would it take Pump A and Pump B working together, each

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