Question

a motor boat whose speed 18 km/hr in still water takes 1hr more to go 24km upstream than to return downstream to the same spot . find the speed of the stream

Answer 1

let speed of stream be x km / hr

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

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

Time taken to travel 24 km in upstream = 24/ (18- x ) hr ( by using distance = speed * time)

Time taken by boat to travel 24 km in downstream = 24/ (18+x) hr

According to question

time taken to travel upstream - time taken to travel downstream = 1

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

By solving

x = 6 km /hr

hope it helps

Answer 2

Answer:

Let the speed of stream be x.

Then,

Speed of boat in upstream is 24 ‒ x

In downstream, speed of boat is 24 + x

According to question,

Time taken in the upstream journey ‒ Time taken in the downstream journey = 1 hour

$\implies\tt \dfrac{32}{24 - x} - \dfrac{32}{24 + x} = 1 \\\\\\\implies\tt\dfrac{24 + x - 24 + x}{{24}^{2} -{x}^{2}} = \dfrac{1}{32} \\\\\\\implies\tt \dfrac{2x}{576 -{x}^{2}} = \dfrac{1}{32}\\\\\\\implies\tt 2x \times 32 = 576 -{x}^{2}\\\\\\\implies\tt {x}^{2} + 64x - 576 = 0\\\\\\\implies\tt {x}^{2} + 72x - 8x - 576 = 0\\\\\\\implies\tt x(x + 72) - 8(x + 72) = 0\\\\\\\implies\tt (x - 8)(x + 72) = 0\\\\\\\implies\tt \green{x = 8} \quad or \quad \red{x =- 72}$

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∴ Speed of the Stream will be 8 km/hr.