Question

A high speed pump can empty 4/7 of a tank in 20 minutes. How many minutes would it take to pump empty an entire tank?

Answer 1

Now, a whole in sevenths, will just be 7/7.

now, we know the pump can do 4/7 of the tank in 20 minutes, how many minutes will it take to do 7/7, or the whole tank?

$\bf \begin{array}{ccll} \stackrel{part}{tank}&minutes\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{4}{7}&20\\\\ \frac{7}{7}&m \end{array}\implies \cfrac{\quad \frac{4}{7}\quad }{\frac{7}{7}}=\cfrac{20}{m}\implies \cfrac{4}{7}\cdot \cfrac{7}{7}=\cfrac{20}{m}\implies \cfrac{4}{7}=\cfrac{20}{m} \\\\\\ 4m=140\implies m=\cfrac{140}{4}\implies m=35$