A man takes 4 hours and 30 minutes to row a boat a distance of 18 km downtream, and 3 hours 30 minutes to row the boat a distance of 7 km upstream. Find the speed of the stream.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 1 km/h.
Let's assume the speed of the boat in still water is 'b' km/h and the speed of the stream is 'c' km/h.
When the boat is traveling downstream, the effective speed of the boat is (b + c) km/h.
Similarly, when the boat is traveling upstream, the effective speed of the boat is (b - c) km/h.
We know that time is taken = distance/speed.
According to the problem,
Time is taken downstream = 4 hours 30 minutes = 4.5 hours.
Distance downstream = 18 km.
Therefore,
(b + c) = distance / time taken downstream = 18 / 4.5 = 4 km/h
Now, Time taken upstream = 3 hours 30 minutes = 3.5 hours.
Distance upstream = 7 km.
Therefore,
(b - c) = distance / time taken upstream = 7 / 3.5 = 2 km/h
Now, let's solve these two equations simultaneously to find the values of 'b' and 'c'.
Adding the two equations, we get:
2b = 6
⇒ b = 3
Substituting the value of 'b' in either of the equations, we get:
⇒ c = 1
Hence, Speed of stream = 1 km/hr