Question

A man rows upstream at 7 km/h and downstream at 10 km/h. Then, the man's speed
in still water and the rate of current respectively, are
(a) 6.5 km/h and 3.5 km/h
(b) 8.5 km/h and 1.5 km/h
(c) 6 km/h and 4 km/h
(d) 7 km/h and 3 km/h​

Answer 1

If a man rows a boat or swims in the direction opposite to the flow of the river, then it is called upstream. Here the speed of the man is less than his speed in still water.

Similarly, downstream is said to be occurred if the man rows a boat or swims in the same direction as that of the river flow. Here the man attains a gain in his velocity than that in still water.

In the case of upstream...

$\setlength{\unitlength}{1mm}\begin {picture}(5,5)\put(0,5){\vector(1,0){25}}\put(25,-5){\vector(-1,0){25}}\put(11.5,7.5){ \vec{v_m} }\put(11.5,-9.5){ \vec{v_r} }\end {picture}$

...since the velocities of river and man, $\vec{v_r}$ and $\vec{v_m}$ respectively, are opposite to each other, and since the speed of the man is 7 km h^(-1) here, we have,

$v_m-v_r=7\quad\longrightarrow\quad (1)$

In the case of downstream...

$\setlength{\unitlength}{1mm}\begin {picture}(5,5)\put(0,5){\vector(1,0){25}}\put(0,-5){\vector(1,0){25}}\put(11.5,7.5){ \vec{v_r} }\put(11.5,-9.5){ \vec{v_m} }\end {picture}$

...since the velocities of river and man are in the same direction, and since the speed of the man is 10 km h^(-1) here, we have,

$v_m+v_r=10\quad\longrightarrow\quad (2)$

Adding (1) and (2), we get the speed of the man in still water, i.e.,

$v_m=\underline{\underline{\mathrm {8.5\ km\ h^{-1}}}}$

On taking difference between (1) and (2), we get the rate of current, i.e., speed of river.

$v_r=\underline {\underline {\mathrm{1.5\ km\ h^{-1}}}}$

Hence (b) is the answer.

#answerwithquality

#BAL

Answer 2

Step-by-step explanation:

b) 8.5 km/h and 1.5km/h.