Question

A motor boat going downstream overcame a raft at a point A. One hour later it turned back and after some time passed the raft at a distance $12Km$ from the point A. Find the river velocity(in Km/hr) assuming the speed of motor boat to be constant.

Answer 1

Since the boat is travelling in the direction of river flow, the velocity of boat will be affected by the river velocity. While coming back, the velocity of the boat will be the difference in boat velocity and water velocity. Make equations using the velocity formula. Then, by substituting the values accordingly and equating them we can find the velocity of the river.
Formula used:
$\text{v = }\dfrac{\text{distance}\left( d \right)}{\text{time}\left( t \right)}$

Complete step by step answer:

Given that,
Let $x$ be the velocity of motor boat, $y$ be the velocity of water, $d$ be the distance travelled by the boat in $\text{60minutes }\left( \text{1hr} \right)$
We have,
Velocity, $\text{v = }\dfrac{\text{distance}\left( d \right)}{\text{time}\left( t \right)}$
Then,
$d=\left( x+y \right)1$ ----------- 1
Assume that, boat meets the raft in time $t$, then the distance covered by the boat during the upward journey in time $t$ is,
$\left( x-y \right)t=d-12=$ ----------- 2
During the total time$1+t$ raft travels $12km$ distance. Then,
$12=y\left( 1+t \right)$ --------------- 3
Substitute equation 3 and 1 in equation 2. We get,
$\left( x-y \right)t=\left( x+y \right)1-y\left( 1+t \right)$
$xt-yt=x+y-y-yt$
Then,
$xt=x$
$t=1hr$
Substitute the above value in equation 3. We get,
$12=y\left( 1+1 \right)$
$y=\dfrac{12}{2}=6Km/hr$
Velocity of river is $6Km/hr$

Note:
If a boat is travelling along the direction of a river flow, the net velocity of the boat will be the sum of its individual velocity and river velocity. And if it is travelling against the river flow, the net velocity of the boat will be different in the boat velocity and river velocity.