Rational and Radical question

Question

A winery has a vat with two pipes leading to it the inlet pipe can fill the vet in five hours while the outlet pipe can empty it in seven hours how long will it take to fill the vet if both pipes are left open

Answer 1

the input pipe fills 1/5 of the vat per hour while the output pipe empties 1/7 of the vat per hour.

Working against each other, the NET result is that 1/5-1/7 = (7-5)/35 = 2/35 of the vat is filled per hour.

So it will take 35/2 hours to fill it up, which is 17 hours and 30 minutes