Question

A motorboat going downstream overcame a raft at a point A; t = 60 minutes later, it turned back and after some time passed the raft at a distance l = 6.0 km from the point A. Find the flow velocity assuming the duty of the engine to be constant.

• A. 1 km/hr
• B. 3 km/hr
• C. 6 km/hr
• D. Data insufficient

Answer 1

The correct option is B

3 km/hr

Now, let's assume the velocity of boat to be v in still water.
While going down stream its velocity will be v + u
$\frac{v_v}{r}$ :: Velocity of boat relative to raft => v + u - u = + v after 1 hr distance between them will be v km.
In 1 hr raft moved by u× 1 = u km
Now while coming back
vb = -(v - u)
vr = + u
$\frac{v_b}{r}$ = - (v - u) - u = - v
So we see here that the relative velocity of boat with respect to raft is same as while going downstream or upstream both.
Now, $\frac{v_b}{r=v}$ distance between them = v km.
So time in which they meet = $\frac{v}{v}=1hr$
So in next 1 hr they meet at some point,which will be 6 km away from A
Also in next 1 hr the raft would have traveled another u km. so total distance of meeting point from A in 2u = 6 ⇒ u = 3 km/hr
Flow velocity = speed of raft = 3 km/hr