Question

A motorboat whose speed in still water is 9km/h, goes 15km downstream and comes back to the same spot, in total time of 3hours 45 minutes. Find the speed of the stream

Answer 1

Question:

A motorboat whose speed in still water is 9km/h, goes 15km downstream and comes back to the same spot, in total time of 3hours 45 minutes. Find the speed of the stream?

Answer:

Let the speed of the steam be x km/hr

◆ Downstream speed = (9+x) km/hr

◆ Upstream speed = (9-x) km/hr

Distance covered downstream = Distance covered upstream = 15 km

Total time taken = 3 hr 45 min

= (3+45/60) minutes

= 225/60 min

= 15/4 min

$\frac{15}{(9 + x)} + \frac{15}{(9 - x)} = \frac{15}{4}$

$\frac{1}{(9 + x)} + \frac{1}{(9 - x)} = \frac{1}{4}$

$\frac{9 - x + 9 + x}{(9 + x)(9 - x)}$

$\frac{18}{ {9}^{2} - {x}^{2} } = \frac{1}{4}$

$\frac{18}{81 - {x}^{2} } = \frac{1}{4}$

$81 - {x}^{2} = 72$

$81 - {x}^{2} - 72 = 0$

$- {x}^{2} + 9 = 0$

${x}^{2} = 9$

$x = 3 \: \: or \: x = - 3$

Therefore, the speed of the stream is 3 km/hr. (The value of x cannot be negative).

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Answer 2

Refers to attachment....!!

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