GMATPREP Constant Rate

[cveluswamy]

At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?


A. 10
B. 12
C. 15
D. 25
E. 50

[jayhawk2001]

You have to use the rate formula here

1/t = 1/t1 + 1/t2 = 1/30 + 1/20 = 1/12

So, 12 minutes

Put another way, in each minute the pipes can fill 1/30 and 1/20 of the
pool respectively. So, combined the hoses can fill (1/30 + 1/20) of the
pool per minute. The reciprocal of this value will give you the time
required to fill the pool when both hoses are used.

[cat er ina]

You have to use the rate formula here

1/t = 1/t1 + 1/t2 = 1/30 + 1/20 = 1/12

So, 12 minutes

Put another way, in each minute the pipes can fill 1/30 and 1/20 of the
pool respectively. So, combined the hoses can fill (1/30 + 1/20) of the
pool per minute. The reciprocal of this value will give you the time
required to fill the pool when both hoses are used.

hi can you explain exactly how you get 12? isn t it: 1/20+ 1/30 = 30+20/60 = 50/60 ?

[gmatmachoman]

You have to use the rate formula here

1/t = 1/t1 + 1/t2 = 1/30 + 1/20 = 1/12

So, 12 minutes

Put another way, in each minute the pipes can fill 1/30 and 1/20 of the
pool respectively. So, combined the hoses can fill (1/30 + 1/20) of the
pool per minute. The reciprocal of this value will give you the time
required to fill the pool when both hoses are used.

hi can you explain exactly how you get 12? isn t it: 1/20+ 1/30 = 30+20/60 = 50/60 ?

@caterina!

U missed the whole point there!!!

It is supposed to be 50 /600 instead of 50/60...( seems u missed a ZERO)!!

It happens....!!!

[cat er ina]

You have to use the rate formula here

1/t = 1/t1 + 1/t2 = 1/30 + 1/20 = 1/12

So, 12 minutes

Put another way, in each minute the pipes can fill 1/30 and 1/20 of the
pool respectively. So, combined the hoses can fill (1/30 + 1/20) of the
pool per minute. The reciprocal of this value will give you the time
required to fill the pool when both hoses are used.

hi can you explain exactly how you get 12? isn t it: 1/20+ 1/30 = 30+20/60 = 50/60 ?

@caterina!

U missed the whole point there!!!


It is supposed to be 50 /600 instead of 50/60...( seems u missed a ZERO)!!

It happens....!!!

OOOPs :roll: thank you!!

[thephoenix]

(20*30)/(20+30)=600/50=12

[dumluck]

Apologies for dragging this question up again but...

If I was to depict this in an RTW table would it look like this?
r . t = w
1 r . 20 = 1
2 r . 30 = 1

r = w/t so 1 = 1/20, 2 = 1/30 but that would be stating a rate of one swimming pool/20 minutes or one swimming pool/30 minutes.

Given the above if you add 1/20 + 1/30 would that not denote how long it would take both to fill two swimming pools instead of what proportion of the one pool would be filled in 1 minute?

I just want to get it clear logically.

Thanks,
D



r =

[GMATGuruNY]

At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?


A. 10
B. 12
C. 15
D. 25
E. 50

Let pool = 60 liters.
Rate for large hose = w/t = 60/20 = 3 liters per minute.
Rate for small hose = w/t = 60/30 = 2 liters per minute.
Combined rate for both hoses working together = 3+2 = 5 liters per minute.
Time for both hoses to fill the pool = w/r = 60/5 = 12 minutes.

The correct answer is B.

[mk101]

At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?


A. 10
B. 12
C. 15
D. 25
E. 50

Let pool = 60 liters.
Rate for large hose = w/t = 60/20 = 3 liters per minute.
Rate for small hose = w/t = 60/30 = 2 liters per minute.
Combined rate for both hoses working together = 3+2 = 5 liters per minute.
Time for both hoses to fill the pool = w/r = 60/5 = 12 minutes.

The correct answer is B.

Mitch, as usual, is spot on .... just adding one thing here -where did that 60 come from? - The volume assumed should be such a number which is a multiple of both 20 and 30,i.e. a common multiple of 20,30.

LCM (20,30) =60