Two water pumps working together at respective constant

Question

Two water pumps working together at respective constant rates took 4 hrs to fill a pool. If constant rate of one pump was 1.5 times the constant rate of the other, then how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?

5
16/3
11/2
6
20/3

I got B, but the answer is E....please explain.

ghantark · Answer

Rate of First Pump = R
Rate of Second Pump = (3/2) R

Work Done = Rate * time

(R + 3/2 R)*4 = 1

R = 1/10

Rate of Fater Pump = (3/2)R = 3/20
Time = W/Rate = 1/(3/20) = 20/3

zorro13 · Answer

HI....

Remember that in this case

1/time machine A + 1/time amchine B = 1/Total time


..

Futuristic · Answer

Let rates per hour be a,b. 
Then, (a+b)4 = full (f)

now let a=1.5b

2.5b. 10 =f

b=f/10.

(a+f/10)4 =f
4a +2f/5 = f
4a = 3f/5

a=3f/20

comparing a and b, we can see a is the faster rated pump.

in 1hr a completes 3/20 of tank
time taken by to complete tank =1/(3/20) = 20/3

rbcola · Answer

I would have used numbers for this one. 

let the smaller pump have a capacity of 200 gallons per hours
Then the faster one is 300 gallons per hour, since it is 1.5 times bigger

Both pump operating for 4 hours will fill up 200*4 + 300*4 = 2000 gallons

You can see the answer the moment you get 2000. The answer is 2000/300 = 20/3

balajinaik · Answer

This is how i calculated. Pls let me know if this is wrong way of doing it.

Formula to find the combined effort of A & B is

AB/A+B
we are given 2 equations.
1. Combined work is 4. so AB/A+B = 4
2. A=1.5B ( Pump A is 1.5 times faster than B)

substituting value of A from equation 2 in equation 1 we get B=20/3

ps_dahiya · Answer

I did it like this:

Faster pump is 1.5 times faster than the slower.
So slower pump will fill in 4 * 5/2 = 10 hours

So faster pump will fill in 10 * 2/3 = 20/3

bondguy · Answer

higher rate lesser time
let speed be x , time = y 

applying inverse proportion

 speed-------------time
 | x + 1.5x---------- 4 ^
 V 1.5 x--- ---------(y) |

Therefore

x(1 + 1.5) 
------------ = y/ 4 
1.5x

y = 20/3

if practised upon, it takes hardly 1 min to get the answer

jaynayak · Answer

E.

Let the slower one can complete 1 work in x hrs
Hence the rate is 1/x

Rate of the faster one is 1.5/x

Given they both working together take 4 hrs

Hence
1/x +1.5/x = 1/4
2.5/x = 1/4
x = 10 
Hence faster one can finish in x/1.5 = 10/1.5 = 20/3

Two water pumps working together at respective constant

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