Work = Rate per hr * Time ....so....
Rate of one pipe * hrs worked + Rate of second pipe * hrs worked = Whole job done
Call x the number of hours it takes one pipe to fill the tank...its rate per hr = 1/x
And the second pipe takes x + 2 hrs.......its rate per hour = 1 /[ x + 2]
Whole job done = 1
So we have
[1/x] * 6 + 1/ [x + 2] *6 = 1
( [6 ( x + 2)] + 6x ) / [ x( x + 2) ] = 1 multiply both sides by x (x + 2)
6x + 12 + 6x = x (x + 2)
12x + 12 = x^2 + 2x rearrange as
x^2 - 10x - 12 = 0 taking the postiive solution for x and we have
x = 5 + √37 hrs ≈ 11.083 hrs and x + 2 ≈ 13.083 hrs
