A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

140 minutes
21 hour
31 hr 15 min
41 hr 30 min

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Rate downstream \\ = (\frac{1}{10} \times 60) k m / h r = 6 k m / h r \\ Rate upstream = 2 k m / h r \\ Speed in still water \\ = \frac{1}{2} (6 + 2) k m / h r = 4 k m / h r \\ ∴ Required time \\ = (\frac{5}{4}) h r s \\ = 1 \frac{1}{4} h r s \\ = 1 h r 15 min . \end{aligned}

$\eqalign{ & {\text{Rate}}\,{\text{downstream}} \cr & = \left( {\frac{1}{{10}} \times 60} \right)km/hr = 6\,km/hr \cr & {\text{Rate}}\,{\text{upstream}} = 2\,km/hr \cr & {\text{Speed}}\,{\text{in}}\,{\text{still}}\,{\text{water}} \cr & = \frac{1}{2}\left( {6 + 2} \right)km/hr = 4\,km/hr \cr & \therefore {\text{Required}}\,{\text{time}} \cr & = \left( {\frac{5}{4}} \right)hrs \cr & = 1\frac{1}{4}hrs \cr & = 1\,hr\,15\,\min . \cr}$