Question

A motor boat covers the distance between two spots on the river in $t_1=8hr$ and $t_2=12hr$ downstream and upstream respectively. The time required for the boat to cover this distance in still water will be-

• A. 6.9 hr
• B. 9.6 hr
• C. 69 sec
• D. 96 sec

Answer 1

Answer: (B)

Let $s$ be the distance between that two spots.
Also assume that the velocity of the motor
boat in still water is $v$ and the velocity of flow of water is $u$.
Then, for downward journey,
$s/t_1=v+u...(A)$
For upward journey,
$s/t_2=v-u...(B)$
Adding eq. (A) to (B),
$s/t_1+s/t_2=2v$
or $t=\frac{s}{v}=\frac{2t_1{t}_2}{\left(t_1+t_2\right)}=\frac{2\times 8\times 12}{(8+12)}$
$=9.6hr$