A boat can go 24km downstream and return in 5 hours. If the speed for the stream is 2km/hr,find the speed of boat in still water.
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Let v = Speed of Jack's boat in still water.
When rowing downstream, the speed of the current is added to the speed of Jack's boat in still water (v) -
Speed of Jack's boat = (v + 2) kmph
Time taken to reach destination = (24 km)/(v + 2 kmph) …….…(A)
When rowing upstream, the speed of the current is subtracted from the speed of Jack's boat in still water (v) -
Speed of Jack's boat = (v - 2) kmph
Time taken to reach starting point from destination = (24 km)/(v - 2 kmph) …….…(B)
Total time taken = (A) + (B) = 9 hours (given)
Simplifying we get,
(3v²/16) - v - (3/4) = 0
Solving for v, we get,
v = 6 or (-2/3)
Hence, speed of Jack's boat in still water = 6 kmph (as speed can't be negative)
Check -
Time taken by Jack to reach destination from starting point = (24 km)/(6+2 kmph) = 3 hours
Time taken by Jack to reach starting point from destination = (24 km)/(6-2 kmph) = 6 hours
Total time taken = 3 + 6 = 9 hours
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When rowing downstream, the speed of the current is added to the speed of Jack's boat in still water (v) -
Speed of Jack's boat = (v + 2) kmph
Time taken to reach destination = (24 km)/(v + 2 kmph) …….…(A)
When rowing upstream, the speed of the current is subtracted from the speed of Jack's boat in still water (v) -
Speed of Jack's boat = (v - 2) kmph
Time taken to reach starting point from destination = (24 km)/(v - 2 kmph) …….…(B)
Total time taken = (A) + (B) = 9 hours (given)
Simplifying we get,
(3v²/16) - v - (3/4) = 0
Solving for v, we get,
v = 6 or (-2/3)
Hence, speed of Jack's boat in still water = 6 kmph (as speed can't be negative)
Check -
Time taken by Jack to reach destination from starting point = (24 km)/(6+2 kmph) = 3 hours
Time taken by Jack to reach starting point from destination = (24 km)/(6-2 kmph) = 6 hours
Total time taken = 3 + 6 = 9 hours
Mark AS BRAINLIST
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