Math, asked by rajivroadlines, 1 year ago

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.

Answers

Answered by YashGandhi
4
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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