Pump A can fill a tank in twelve minutes. Pump B can fill the same tank in 20 minutes.?

Question

Working together, how long would it take the two pumps to fill one tank? Then answer in 7 1/2 minutes. Show the work of how to get the answer of 7 1/2.

Answer 1

We'll say that the volume of the tank is V. The rate at which pump A pumps is V/12. The rate at which pump B pumps is V/20. So, the total volume after a certain time, t, would be:
(V/12)t + (V/20)t

Now, we want to find the amount of time it would take to get to the total volume of the original tank, which we called V:
V*t/12 + V*t/20 = V
V*t(1/12 + 1/20) = V
t(5/60 + 3/60) = 1
t(8/60) = 1
t = 60/8 = 7 1/2

So it takes 7 1/2 minutes to fill the tank.

Answer 2

Let the capacity of the tank is X
Pump A in 1 minute will fill the tank X/12 part and pump B in 1 minute will fill the tank X/20 part.If both the pumps are working together we will arrive at the equation as below
X/12+X/20 part of the tank will get filled =in1Minute
By solving the equation as under
5X/60+3X/60 =1
8X/60 =1
8X= 60
X=60/8
X= 71/2 minutes

Answer 3

Let the volume of the tank be V
Let pump A have a flowrate of q1
Let pump B have a flowrate of q2

Clearly V = 12q1 = 20q2 .....eqn 1

Find t such V = (q1 + q2)t. On rearrangement and equating volumes

V = q2(q1/q2 + 1)t = 20 q2 ..... eqn 2

From eqn 1 q1/q2 = 5/3. Substituting into eqn 2

(5/3 + 1)t = 20 which leads to t = 3 x 20 / 8 = 7.5 minutes

Answer 4

i remember this problem well. It's a shame they can't come up with new ones though. i can even remember the formulation ; have a good time with this one, it's one of my favorites