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Difficulty:
95%
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Question Stats:
42% (02:40) correct
58%
(02:43)
wrong
based on 86
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A man is travelling on a boat upstream a certain river. When he goes under a bridge he is distracted and drops a bottle of whisky into the water without realising. The bottle floats downstream while the man travels upstream for 20 minutes. Then he realises that he had dropped the bottle. He turns back (neglect the time for this operation) and travels downstream at the same speed in respect to the water. He reaches the bottle 1 kilometre downstream from the bridge. What is the speed of the water of the river in km/h?
A. 1 km/h
B. 1.5 km/h
C. 2 km/h
D. 2.5 km/h
E. 3 km/h
A. 1 km/h
B. 1.5 km/h
C. 2 km/h
D. 2.5 km/h
E. 3 km/h
04 Aug 2023, 13:29
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Rm = boat speed
Rw = water speed
He heads upstream for 20 minutes at a speed of Rm-Rw before turning around, so he travels upstream:
20(Rm-Rw)
The bottle has traveled
20Rw downstream in that 20 minutes
Upon turning around, the man has to travel the distance between him and the bottle and is now going at a speed of Rm + Rw, with distance of:
20(Rm-Rw)+ 20Rw
and is closing in on the bottle at a speed represented by their difference in speeds:
(Rm+Rw)-Rw
So the time to cover this distance is distance/rate:
t = [20(Rm-Rw) + 20Rw]/[(Rm+Rw)-Rw] =
20Rm/Rm = 20 minutes
So the man travels downstream for the same amount of time he traveled upstream !
So the total time elapsed is
40 minutes,
during which time the bottle has traveled 1km downstream.
So the rate of speed of the stream must be:
1/(40/60) = 3/2 = 1.5km/hr
Posted from my mobile device
Rw = water speed
He heads upstream for 20 minutes at a speed of Rm-Rw before turning around, so he travels upstream:
20(Rm-Rw)
The bottle has traveled
20Rw downstream in that 20 minutes
Upon turning around, the man has to travel the distance between him and the bottle and is now going at a speed of Rm + Rw, with distance of:
20(Rm-Rw)+ 20Rw
and is closing in on the bottle at a speed represented by their difference in speeds:
(Rm+Rw)-Rw
So the time to cover this distance is distance/rate:
t = [20(Rm-Rw) + 20Rw]/[(Rm+Rw)-Rw] =
20Rm/Rm = 20 minutes
So the man travels downstream for the same amount of time he traveled upstream !
So the total time elapsed is
40 minutes,
during which time the bottle has traveled 1km downstream.
So the rate of speed of the stream must be:
1/(40/60) = 3/2 = 1.5km/hr
Posted from my mobile device
23 Oct 2024, 04:34
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