A man rows 12 km in 5 hours against the stream and the speed of current being 4 kmph. What time will be taken by him to row 15 km with the stream?

11hour 27⁷/₁₃ minutes
21hour 24⁷/₁₃ minutes
31hour 25⁷/₁₃ minutes
41hour 26⁷/₁₃ minutes

Answer:- 1

Explanation:-

Solution:

\begin{aligned} According to question \\ Speed of current y = 4 k m / h \\ Distance  = 12 k m \\ Speed in upstream \\ = (x - y) k m / h r . \\ Here x is speed of boat in still water \\ = \frac{Distance}{Time} \\ x - 4 = \frac{12}{5} \\ 5 x - 20 = 12 \\ 5 x = 32 \\ x = 6.4 k m / h r \\ Speed in downstream \\ = (x + y) = 6.4 + 4 \\ = 10.4 k m / h \\ ∴ Time  = \frac{Distance}{Speed} \\ Time  = \frac{15}{10.4} = \frac{150}{104} \\ = 1 hour 26 \frac{7}{13} minutes \end{aligned}

$\eqalign{ & {\text{According to question}} \cr & {\text{Speed of current }}y = {\text{ }}4{\text{ }}km/h \cr & {\text{Distance = }}12{\text{ }}km \cr & {\text{Speed in upstream }} \cr & {\text{ = }}\left( {x - y} \right)km/hr. \cr & {\text{Here }}x{\text{ is speed of boat in still water}} \cr & \,{\text{ = }}\frac{{{\text{Distance}}}}{{{\text{Time}}}} \cr & x - 4 = \frac{{12}}{5} \cr & 5x - 20 = 12 \cr & 5x = 32 \cr & x = 6.4\,km/hr \cr & {\text{Speed in downstream }} \cr & {\text{ = }}\left( {x + y} \right) = 6.4 + 4 \cr & = 10.4\,km/h \cr & \therefore {\text{Time = }}\frac{{{\text{Distance}}}}{{{\text{Speed }}}} \cr & {\text{Time = }}\frac{{15}}{{10.4}} = \frac{{150}}{{104}} \cr & = 1\,{\text{hour}}\,\,26\frac{7}{{13}}\,\,{\text{minutes}} \cr}$