Working at constant rate, pump X pumped out half of the water in a flo

Question

Working at constant rate, pump X pumped out half of the water in a flooded basement in 4 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?

a. 10
b. 12
c. 14
d. 18
e. 24

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a. 10
b. 12
c. 14
d. 18
e. 24

gracie · Accepted Answer

rate of x=1/8
rate of x+y=1/6
rate of y=1/6-1/8=1/24
24 hours

mahfuz_fahim · Answer

Here pump x was able to work 1/2 the job in 4 hrs.

so it would have taken the pump x to complete the task in 8 hrs.  so 1/x=1/8.....eqn(1)

again x and y working independently doing the same work (1/2 of the work) take 3hrs. 
 so total task would take 6 hrs. 1/x+1/y=1/6.........eqn(2)

solve eqn 1 and eqn 2 to get y=24

Bunuel · Answer

Almost the same question to practice: https://gmatclub.com/forum/working-alon ... 16023.html Hope it helps.

pushpitkc · Answer

If the pump X pumped out half the water in 4 hours, it will pump out the entire water in 8 hours. 
Similarly, the pump Y was started and the two pumps operating together are able to pump out 
the entire water in 3 hours. 
 
Assume the total capacity of the pump to be 96 units.

So, the pump X must be pumping out 12 units/hour. Since, both the pumps working together 
pump out the remainder of the water in 3 hours, their combined capacity will be 16 units/hour. 
Hence, pump Y must be pumping out 4 units/hour.

Therefore, Pump Y alone will take  \frac{96}{4}  =  24 hours(Option E)

Nived · Answer

Suppose X extracts x liters/hour, while Y extracts y liters/hour
In 4 hours, X extracts 4 x liters
This is half of the basement capacity. So, total volume of water in the basement = 8x liters

After 4 hours, Y was started as well. They flush the remaining 4 x in 3 hours.

In 3 hours, X and Y combined would flush 3*(x + y)

It is given that 3*(x + y) = 4x
This gives x = 3y

Operating alone how much would Y take?

Total water = 8x
Y's capacity = y liters/hour

So, time taken by Y = 8x/y

We know x = 3y
So, x/y = 3

So, time taken by Y = 8x/y = 8*3 = 24

gulyaa · Answer

Trying plugging:

We are looking at half capacities throughout the problem, so we could half the answer choices for simplicity. If X = 4h -> rate = 1/4; X + Y = 3h -> rate = 1/3. We can start plugging answer choices from B:

B: 12 -> 6 h -> 1/6 + 1/4 = 5/12 - almost 1/2 or too big for the 1/3 we need, that means we need a smaller Y rate or higher Y hours
D: 18 -> 9 h -> 1/9 + 1/4 = 13/36 - if we compare with 1/3 or 13/39, 13/ 36 is still a bit big, but closer to what we need -> answer E

hero_with_1000_faces · Answer

A alternative approach:

We can infer that x takes 8 hours to remove water completely, now:

We see that X worked 7 hours - 4+3 hours, and was left with only one hours of work.

For that 1 hour of work Y took 3 hours, so for 8 hours of X's work Y will take 8*3 = 24 hours

kritisachan · Answer

pump x was able to do 1/2 of the job in 4 hrs  
pump x would do the entire work alone in 1/8 hrs
therefore, 1/x = 1/8 ---  eqn (1)

since x and y are now working together, they finish the entire thing in 3 hrs
total time taken would be 6 hrs

pump x + pump y = 1/x + 1/y= 1/6 ----  eqn (2)

1/8+ 1/y = 1/6
1/y = 1/6- 1/8
1/y = 8-6/48
1/y = 1/24

therefore,  y = 24

msignatius · Answer

1/2 the water pumped out from the flooded basement in 4 hours? That's 1/2*1/4 = 1/8 water pumped out every hour - pace of pump X.

Pump Y starts pumping the remaining 1/2 water out simultaneously with pump X. We know pump X has a pace of 1/8 water pumped out every hour. 4/8 remain (the remaining half). In 3 hours, X will pump out 3/8 of this remaining 4/8. Which means, pump Y will pump out just 1/8 water in 3 hours. Or 0.33 / 8 water in an hour, or 1/24 water an hour.

Now, if we're to let pump Y do all 100% of the pumping-out, from the start, as evidenced by the 1/24 above, we'll need 24 hours to get the job done. E.

Usernamevisible · Answer

LCM METHOD (WORK PROBLEMS)

Same work = half of the water

X alone → 4 hours → does 1 half
X + Y → 3 hours → does 1 half

LCM of 4 and 3 = 12 hours

In 12 hours:
X alone → 3 halves
X + Y → 4 halves

Y alone = (X + Y) − X
= 4 halves − 3 halves
= 1 half in 12 hours

So Y does full work in = 24 hours

Answer: 24

Working at constant rate, pump X pumped out half of the water in a flo

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Working at constant rate, pump X pumped out half of the water in a flo

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