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cluponka [151]
2 years ago
11

A fisherman traveled in a boat from point N upstream. After having traveled 6 km, he stopped rowing and 2 hour 40 min after firs

t leaving N, he was brought back to N by the current. Knowing that the speed of the boat in still water is 9 km/hour, find the speed of the river’s current.
Mathematics
1 answer:
Nat2105 [25]2 years ago
6 0

Answer:

The speed of the river's current is 4.5 km/hr.

Step-by-step explanation:

Given : A fisherman traveled in a boat from point N upstream.

After having traveled 6 km, he stopped rowing and 2 hour 40 min after first leaving N, he was brought back to N by the current.

Knowing that the speed of the boat in still water is 9 km/hour

To find : The speed of the river’s current.

Solution :

Let the speed of current  = x km/h

Speed of boat = 9 km/h

Thus, the speed in upstream = (9 - x) km/h

Also, the speed in downstream = x km/h (because the boat is stationary in downstream)

Total distance = 6 km ( from N to the point he reached )

Total time = 2 hours 40 minutes

\text{2 hours 40 minutes}=2\frac{40}{60}=2 \frac{2}{3} \\\\\text{2 hours 40 minutes}=\frac{8}{3} \text{ hours}

We know, \text{Time} = \frac{\text{Distance}}{\text{Speed}}

According to the question,

\frac{6}{9-x}+\frac{6}{x}=\frac{8}{3}

Taking LCM and 6 common

6[\frac{x+9-x}{(9-x)x}]=\frac{8}{3}

Take 6 to another side,

\frac{9}{9x-x^2}=\frac{8}{3\times 6}

Cross multiply,

9\times 18=8\times(9x-x^2)

162=72x-8x^2

Taking 4 common and cancel out

4x^2-36x+81=0

Solve quadratic equation by middle term split,

4x^2-18x-18x+81=0

2x(2x-9)-9(2x-9)=0

(2x-9)(2x-9)=0

\Rightarrow 2x-9=0

\Rightarrow x=\frac{9}{2}=4.5

Therefore, The speed of the river's current is 4.5 km/hr.

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