# math

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A tank fitted with two pipes is to filled with water. One pipe can fill it in 5 hours. After it has been open for 3 hours, the second pipe is opened and the tank is filled in 4 hours more. How long it would take the second pipe alone to fill the tank?

• math -

let the tank contain V units of volume

rate of first pipe = V/5 units/hr
rate of 2nd pipe = V/x units/hr

So the first pipe runs for 3 hrs
Volume = 3(V/5) = 3V/5
the second pipe runs for 4 hrs.
Volume filled by 2nd pipe = 4(V/x) = 4V/x

3V/5 + 4V/x = V
multiply by 5x
3Vx + 20V = 5xV
3x + 20 = 5x
x = 10

It would take 10 hrs using the 2nd pipe alone

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