Question

Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

Answer 1

That's easy!

If the water is standing still the speed of the boat is 9kmph and the stream's speed is 1.5kmph.

When the boat goes in the direction​ of stream, the stream speed adds up with boat speed, and helps moves faster. Pretty intuitive, right?

Therefore, for one side of the journey, the relative velocity of the boat wrt ground will be (9+1.5)= 10.5m/s

Similarly, when the boat goes opposite to the direction of motion, the stream speed is subtracted from the boat speed.

Therefore, for other side of the journey, the relative velocity of the boat wrt ground will be (9-1.5)= 7.5m/s

For both sides of the journey, the boat travels 105 km. So, we can easily calculate the time for both the journeys.

For one side,
t1 = distance / speed
t1 = 105/10.5 = 10sec

For other side,
t2 = distance / speed
t2 = 105/7.5 = 14sec
The total time taken for the whole journey is the sum of these two times.
T = t1+ t2 = 10+14
T = 24 s

Hope you understand the concept.
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