A large pipe can fill a tank 10 minutes faster than it takes a smaller pipe to fill the same tank. Working together, both pipes can fill the tank in 12 minutes. How long would it take the large pipe working alone to fill the tank?

Answer 1

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Answer 2

time to fill with smaller pipe --- x minutes
rate of smaller pipe = 1/x units/min

time to fill with larger pipe --- x-10 minutes
rate of larger pipe = 1/(x-10) units/min

combined rate = 1/x + 1/(x-10)
= (x-10 + x)/(x(x-10))
= (2x-10)/(x^2 - 10x)

1/[ (2x-10)/(x^2 - 10x)] = 12
(x^2 - 10x)/(2x-10) = 12
x^2 - 10x = 24x - 120
x^2 - 34x + 120 = 0
using the formula,
x = (34 ± √676)/2
= 30 minutes or 4 minutes, but x > 10

so the time to fill with the smaller pipe = 30 minutes
and the time to fill with the larger pipe is 20 minutes

check:
is the time of one more than the other equal to 10 minutes ? yes
comined rate
= 1/30 + 1/20 = 50/600 = 1/12
so time to do with combined rate = 1÷(1/12) = 12
My answer is correct.

Answer 3

pipe A fill the tank in 10m and pipe B can fill the tank in 15m then how long it will take to fill the tank by both A and B