On a river , Q is the mid - point between two points P and R on the same bank of the river. A boat can go from P to Q and back in 12 hours, and from P to R in 16 hours 40 minutes. How long would it take to go from R to P?

Explanation:-

$$\eqalign{ & {\text{P - - - - - - - - - - - - }}\mathop {\text{ - }}\limits_{\text{Q}} {\text{ - - - - - - - - - - - - R}} \cr & {\text{ < - - - - - - - 16}}{\text{.40 - - - - - - - > }} \cr & \because {\text{Time required travelling from P to R}} \cr & {\text{ = 16H 40M}} \cr & \because {\text{PQ = QR}}\left( {\because {\text{Q is mid point}}} \right){\text{ }} \cr & {\text{Required time to travel PQ}} \cr & {\text{ = }}\frac{1}{2}\left( {{\text{16H 40M}}} \right) = \,\,{\text{8H 20M}} \cr & {\text{total required time from}} \cr & {\text{P to Q + Q to P = 12H}} \cr & {\text{ = 8H 20M + Q to P = 12H}} \cr & {\text{Time Q to P}} \cr & {\text{ = 12H - 8H 20M}} \cr & {\text{ = 3H 40M}} \cr & \because \overrightarrow {{\text{QP}}} {\text{ = }}\frac{1}{2}\overrightarrow {{\text{RP}}} {\text{ }}\,\,\left( {{\text{Distance}}} \right) \cr & \therefore {\text{Required time to }}\overrightarrow {{\text{RP}}} {\text{ }} \cr & {\text{ = 2}} \times \left[ {\overrightarrow {{\text{QP}}} } \right] \cr & {\text{ = 2}}\left[ {3{\text{H 40M}}} \right]{\text{ }} \cr & {\text{ = 7 H 20M}} \cr & {\text{ = 7}}\frac{1}{3}{\text{Hr}}{\text{. }} \cr}$$