Question

A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 5 ​hours, while the outlet pipe can empty it in 8 hours. How long will it take to fill the vat if both pipes are left​ open?

Answer 1

Answer:

                 $time=40/3hours\approx 13.3hours$

Step-by-step explanation:

The rates are additive: you can calculate the inlet rate and the outlet rate and add them algebraically, i.e. the inlet rate will be positive and the outlet rate will be negative.

1. Inlet rate:

$1vat/5hours$

2. Outlet rate:

$1vat/8hours$

3. Net rate:

            $\text{Inlet rate - outlet rate}=1vat/5hours-1vat/8hours\\\\ \text{Net rate}=(8-5)vat/40hour=3vat/40hour=(3/40)vat/hour$

4. Time to fill the vat

           $rate=amount/time\implies time=amount/rate\\ \\ time=1vat/(3vat/40hour)$

          $time=40/3hours\approx 13.3hours$