Question 1003410
A small pipe can fill a tank in 8 min more time than it takes a larger pipe to fill the same tank.
 Working together, the pipes can fill the tank in 3 min.
 How long would it take each pipe, working alone, to fill the tank? 
:
let t = time for the larger pipe to fill the tank alone
then
(t+8) = time for the smaller pipe to do it
:
let the completed job = 1 (a full tank)
{{{3/t}}} + {{{3/((t+8))}}} = 1
multiply by t(t+8), cancel the denominators and you have
3(t+8) + 3t = t(t+8)
3t + 24 + 3t = t^2 + 8t
Combine like terms on the right
0 = t^2 + 8t - 6t - 24
A quadratic equation
t^2 + 2t - 24 = 0
Factors to
(t+6)(t-4) = 0
We only want the positive solution here
t = 4 min for the larger pipe to fill the tank
:
:
Check solution (small pipe requires 12 min)
{{{3/4}}} + {{{3/12}}} = 1