Question

Three spraying machines working together can finish painting a house in 60 minutes. How long will it take for 5 machines of the same capacity to do the same job?

Answer 1

Let the time taken by 5 spraying machines to finish a painting job be x minutes.

Number of machines	3	5
Time (in minutes)	60	x

$$\begin{gathered} \mathrm{Since}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{spraying}\mathrm{machines}\mathrm{and}\mathrm{the}\mathrm{time}\mathrm{taken}\mathrm{by}\mathrm{them}\mathrm{to}\mathrm{finish}\mathrm{a}\mathrm{painting}\mathrm{job}\mathrm{are}\mathrm{in}\mathrm{inverse}\mathrm{variation},\mathrm{we}\mathrm{have}: \\ 3\times 60=5\times x \\ \Rightarrow 180=5x \\ \Rightarrow x=\frac{180}{5} \\ =36 \\ \mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{time}\mathrm{will}\mathrm{be}36\mathrm{minutes}. \end{gathered}$$