A motorboat going downstream overcame a raft at a point A at t = 0. After 30 min, engine of boat shutdown due to some fault. The man on the boat repairs the engine and it takes 30 min. The boats starts and turn back. After sometime, it passes the raft at a distance 21/2 km from the point A. Find the flow velocity of stream in km/h. (Assume velocity of motorboat constant with respect to river flow)
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Answers
Given : A motorboat going downstream overcame a raft at a point A at t = 0.
After 30 min, engine of boat shutdown due to some fault.
The man on the boat repairs the engine and it takes 30 min.
The boats starts and turn back.
After sometime, it passes the raft at a distance 21/2 km from the point A.
To Find : the flow velocity of stream in km/h.
Solution:
Let say velocity of stream = S km/hr
and Velocity of boat in still water = B km/hr
30 mins + 30 mins = 1 hr
Distance covered by raft in 1 hr = S * 1 = S km
Distance Covered by boat in 1 hr = (B + S) * 1/2 + S/2
( as for 30 min = 1/2 hr with Boat + Stream speed and rest 30 mins = 1/2 hr for stream speed only as boat not working )
= B/2 + S km
Hence Distance between boat and raft = B/2 + S - S
= B/2 km
let say After t hrs they meet as 21/2 km from point A
in this t hrs boat and raft cover together total Distance between them = B/2.
Boat is now upstream hence boat speed = B - S km/hr
=> (B - S) t + S * t = B/2
=> Bt = B/2
=> t = 1/2
Total Time = 1 + 1/2 = 3/2 hrs
Distance covered by raft in 3/2 hrs is 21/2 km
S * 3/2 = 21/2
=> S = 7
Hence velocity of stream in km/h. = 7
( Note : Raft has no motor so it moves with stream velocity only )
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