A reservoir is fed by two pipes of different diameter. The pipe with the larger diameter takes three hours less than the smaller pipe to fill the reservoir. if both pipes are opened simultaneously, the reservoir can fill in two hours. Calculate how long it takes the pipe with the larger diameter to fill the reservoir on its own
QB = flow rate through big pipe
QB = 1 res /t hours
QS = flow rate through small pipe
QS = 1 res / (t+3) hours
2 (QB+QS) = 1 res
2 [ 1/t + 1/(t+3) ] = 1
2(t+3) + 2 (t) = t^2 + 3 t
2 t + 6 + 2 t = t^2 + 3 t
t^2 - t -6 = 0
(t-3)(t+2) = 0
t = 3