A motorboat in still water travels at a speed of 36 km/hr. It goes 56 km upstream in 1 hour 45 monutes. The time taken by it to cover the same distance down the stream will be-

A motorboat in still water travels at a speed of 36 km/hr. It goes 56 km upstream in 1 hour 45 monutes. The time taken by it to cover the same distance down the stream will be- Correct Answer 1 hour 24 minutes

$$\eqalign{ & {\text{Speed upstream}} \cr & {\text{ = }}\left( {\frac{{56}}{{1\frac{3}{4}}}} \right)km/hr \cr & = \left( {56 \times \frac{4}{7}} \right)km/hr \cr & = 32km/hr \cr & {\text{let speed downstream be }}x{\text{ km/hr}}{\text{.}} \cr & {\text{Then speed of boat in still water }} \cr & {\text{ = }}\frac{1}{2}\left( {x + 32} \right)km/hr \cr & \therefore {\text{ }}\frac{1}{2}\left( {x + 32} \right) = 36\,\,\, \Rightarrow x = 40 \cr & {\text{Hence , required time}} \cr & {\text{ = }}\left( {\frac{{50}}{{40}}} \right)hrs \cr & = 1\frac{2}{5}hrs \cr & = 1\,{\text{hour}}\,24\operatorname{minutes} \cr} $$