Question

the speed of boat in still water is 15kmh it can go 30km upstream and return downstream to original point in 4hr and 30 min.
find speed of stream.​

Answer 1

The speed of the stream is 5 km/hr.

Step-by-step explanation:

The speed of the boat in still water = 15 km/hr

The distance covered by the boat while going upstream or downstream = 30 km

Time taken for the whole journey i.e., upstream and return downstream = 4 hr 30 min

Let the speed of the stream be “x” km/h.

So,

Downstream speed = [15+x] km/h

And,

Upstream speed = [15-x] km/h

Therefore,  we can write the equation as,

$\frac{30}{15+x} + \frac{30}{15-x} = 4 \frac{1}{2}$

⇒ $30 [\frac{1}{15+x} + \frac{1}{15-x}] = \frac{9}{2}$

⇒ $30 [\frac{15 - x + 15 +x}{225 - x^2} ] = \frac{9}{2}$

⇒  $\frac{900}{225 - x^2} = \frac{9}{2}$

⇒ 200 = 225 – x²

⇒ x² = 25

⇒ x = 5 km/hr

Thus, the speed of the stream is 5 km/h.

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