How many hours will it take 3 pumps to empty a tank containing 60,000 litres of water?

Pumps	Litres	Hours
7	75,000	4
3	60,000	\(x \)

As the number of pumps has decreased, we will require more time. Therefore, from the numbers in the first column, we create the fraction that is greater than 1 (i.e. \( \frac{7}{3} \))

As the number of litres has decreased, we will require less time. Therefore, from the numbers in the second column, we create the fraction that is less than 1 (i.e. \( \frac{60,000}{75,000} \))

\begin{align} So \quad x & =\frac{7}{3}\ \times\ \frac{60,000}{75,000}\ \times\ 4 \\ \\ & = \frac{7}{3}\ \times\ \frac{4}{5}\ \times\ 4 \\ \\ & = \frac{112}{15} \\ \\ & = 7.4\dot{6}\ hours \end{align}

How many pumps will be needed to empty a tank of 90,000 litres in 3 hours?

Pumps	Litres	Hours
7	75,000	4
\(x \)	90,000	3

As the number of litres has increased, we will require more pumps. Therefore, from the numbers in the second column, we create the fraction that is greater than 1 (i.e. \( \frac{90,000}{75,000} \))

As the number of hours has decreased, we will require more pumps. Therefore, from the numbers in the third column, we create the fraction that is greater than 1 (i.e. \( \frac{4}{3} \))

\begin{align} So \quad x & =\frac{90,000}{75,000}\ \times\ \frac{4}{3}\ \times\ 7 \\ \\ & = \frac{6}{5}\ \times\ \frac{4}{3}\ \times\ 7 \\ \\ & = \frac{56}{5} \\ \\ & = 11\ \frac{1}{5} \quad pumps \\ \end{align}

But as a part-pump is nonsense, we need 12 pumps