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If the speed of a boat in still water is 10 km/hr and the speed of the stream is 2 km/hr, how long will it take to go 24 km downstream?
1.5 ┬аhours
2 ┬аhours
2.5 ┬аhours
3 ┬аhours
2 ┬аhours
Calculate Downstream Speed (DS) by simply adding the boat and stream speeds: 10+2=12 km/hr. Then, mentally divide total distance by DS: 24/12=2.
Speed of boat in still water (u) = 10 km/hr, Speed of stream (v) = 2 km/hr, Distance (d) = 24 km
t=u+vdтАЛ
Calculate Downstream Speed (DS) by simply adding the boat and stream speeds: 10+2=12 km/hr. Then, mentally divide total distance by DS: 24/12=2.
Many students subtract the stream speed instead of adding it (using upstream speed instead of downstream speed), leading to an incorrect result of 24/(10тИТ2)=3 hours.
Calculate downstream speed
Downstream speed is the sum of the boat speed and stream speed.
DS=10+2=12┬аkm/hr
Apply time formula
Time is defined as the ratio of distance to speed.
t=1224тАЛ
Final calculation
Solving the division gives the time taken in hours.
t=2┬аhours
B is correct because the downstream speed is 12┬аkm/hr, and dividing the distance of 24┬аkm by this speed results in exactly 2┬аhours.
This concept of relative speed is identical to solving 'train crossing' problems; remember that when moving in the same direction, speeds add up, and when moving in opposite directions, relative speed is the difference.
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