Question

A bus covers a certain distance with uniform speed. If the speed of the bus would have been increased by 15 km/h, it would have taken two hours less to cover the same distance. And if the speed of the bus would have been decreased by 5 km/h, it would have taken one hour more to cover the same distance. Find the distance covered by the bus.

Answer 1

Let the speed of the bus be x km/h and the time taken be y hours.
Then distance = xy km
According to question, we have:
$$\begin{gathered} \left(x+15\right)\left(y-2\right)=xy \\ \Rightarrow xy-2x+15y-30=xy \\ \Rightarrow -2x+15y=30...\left(1\right) \\ \left(x-5\right)\left(y+1\right)=xy \\ \Rightarrow xy+x-5y-5=xy \\ \Rightarrow x-5y=5...\left(2\right) \\ \mathrm{Multiplying}\mathrm{equation}\left(2\right)\mathrm{by}2,\mathrm{we}\mathrm{get}: \\ 2x-10y=10...\left(3\right) \\ \mathrm{Adding}\mathrm{equation}\left(1\right)\mathrm{and}\left(3\right),\mathrm{we}\mathrm{get}: \\ -2x+15y=30 \\ \underline{2x-10y=10} \\ 5y=40 \\ \Rightarrow y=8 \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}y\mathrm{in}\mathrm{equation}\left(1\right),\mathrm{we}\mathrm{get}: \\ -2x+15\times 8=30 \\ \Rightarrow -2x+120=30 \\ \Rightarrow -2x=30-120 \\ \Rightarrow -2x=-90 \\ \Rightarrow x=45 \\ \therefore \mathrm{Total}\mathrm{distance}=xy=45\times 8=360\mathrm{km} \end{gathered}$$