How long would the smaller one​ take, working​ alone, to fill the​ tank?

Question

Two pipes are connected to the same tank. When working​ together, they can fill the tank in 8 hrs. The larger​ pipe, working​ alone, can fill the tank in 12 hrs less time than the smaller one. How long would the smaller one​ take, working​ alone, to fill the​ tank?

The smaller pipe takes ______ hrs to fill the tank.

Answer 1

Assuming that whole work is 1. If small pipe works alone, it spent X hr, while for the big pipe, working alone, it takes x-12.

Small pipe makes 1/X per hour, the big makes hourly 1 / x-12. But they both make 1 /8 per hour working together.

1/x + 1/ x-12 = 1/8

X2 - 28 X + 96= 0

now need to find roots.