kaplan test problem

[mitaliisrani]

Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates , the swimming pool is filled in 56minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3 . How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate

A) 2hrs,48mins
B) 6hrs, 32mins
C) 7hrs, 12mins
D) 13hrs, 4mins
E) 14hrs, 24mins

OAB

[selango]

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[Testluv]

Let Pump 3 contribute "x" units of work per any unit of time.

Then, Pump 2 contributes 2x while Pump 1 contributes 4x.

For a total of x+2x+4x = 7x.

Thus, Pump 3 contributes x/7x or 1/7 of total work. Thus, working by itself, Pump 3 would take 7*56 minutes or just under 7 hours to complete the job.

Choose B.

[Geva@EconomistGMAT]

Similar approach, only using plugging in numbers and ballparking instead of 'x':

plug in 1,2 and 4 liters/hour for the rates of pumps 3, 2 and 1, respectively. The combined rate is 1+2+4 liters/hour, and together they work for 56 minutes = almost an hour, making the WORK at just under 7 liters (rate*time=work).

Once you have the work and pump 3s rate, find the time: an amount of just under 7 liters at 1 liter/hour will take just under 7 hours.

The benefit of this approach is that it uses 'real' numbers instead of abstract variables. filling a a pool of 7 liters at 1 liter/hour is something you can 'visualize', while many people find a rate of x liters/hour harder to wrap their head around.

[Scott@TargetTestPrep]

Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates , the swimming pool is filled in 56minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3 . How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate

A) 2hrs,48mins
B) 6hrs, 32mins
C) 7hrs, 12mins
D) 13hrs, 4mins
E) 14hrs, 24mins

We can let n = the number of minutes it takes for pump 3 to fill the pool alone. Thus, the rate of pump 3 is 1/n, and that of pump 1 is 4/n and that of pump 2 is 2/n.

Since they can fill the pool in 56 minutes when they work together, their combined rates can be equated as follows:

4/n + 2/n + 1/n = 1/56

7/n = 1/56

n = 7 x 56

n = 392 minutes

Since 1 hour = 60 minutes, 392 minutes = 360 minutes + 32 minutes = 6 hours 32 minutes.

Answer:B

[DrMaths]

56 * (1+2+4) = 56 * 7 < 60mins * 7
So the answer is between 6 and 7 hours
Only answer B matches this criteria