The speed of a boat named Maria in still water is 20 km/hr, while that of boat named Kate is 16 km/hr. The speed of stream is 6 km/hr. Both boats start from the same side of stream at the same point and cross the 20 km wide stream. What will be the distance between the points where they will reach on opposite side of stream?
Solution
Correct Answer: Option B
As per given information,
Speed of boat Maria in still water = 20 km/hr
Speed of boat Kate in still water = 16 km/hr
Speed of stream = 6 km/hr
Now, when the boats will cross the stream, they will cross stream at their own speed. During the time they will cross the stream, they will also move in the direction of stream with the speed of stream. Due to this, the boats will not reach the opposite end of stream at opposite point from where they started. Both these speeds are in perpendicular directions, so we can consider their motion differently.
We know, Time = Distance/Speed
For boat Maria,
Time taken to cross the stream = Width of stream/ Speed of boat Maria in still water
= 20 km/(20 km/hr) = 1 hr
Distance covered by boat Maria along the stream = Time taken × Speed of stream
= 1 hr × 6 km/hr = 6 km
Similarly, for boat Kate,
Time taken to cross the stream = Width of stream/Speed of boat Kate in still water
= 20 km/ (16 km/hr) = 1.25 hr
Distance covered by boat Kate along the stream = Time taken × Speed of stream
= 1.25 hr × 6 km/hr = 7.5 km
∴ Distance between the points where they will reach on opposite side of stream = 7.5 km – 6 km = 1.5 km
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