Question

A motor boat whose speed is 9km/hr in still water takes 1 hour more to go 12 km

upstream than to return downstream to the same spot . Find the speed of the stream.​

Answer 1

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T = time for downstream,

t = time for upstream travel.

T + t = 3 hrs 45 min = 15/4 hrs.

For downstream, distance/velocity = time,

15/(V + v) = T

15/(9 + v) = T ... (1)

Similarly,

15/(9 - v) = t ... (2) ,where V - Speed of boat, v - speed of stream.

Add (1) and (2)

15/(9 + v) + 15/(9 - v) = T + t

15(18)/(81 - v2) = 15/4

v2 = 81 - (18x4) = 9

v = sped of stream is 3 km/hr.

Answer 2

Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

24/(18 - x) = 1 + 24/(18 + x)

24/(18 - x) - 24/(18 + x) = 1

x2 + 48x - 324 = 0

(x + 54)(x - 6) = 0

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream = 6 km/hr