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Johnny and his father go fishing at 5:00 AM. After motoring 6 km upstream, Johnny writes a letter to his friend, puts the letter in a bottle, and drops it into the river. The bottle floats in the current and reaches at 7:40 AM the point where Johnny and his father began their trip. If the speed of the boat in still water is 9 km/h, what is the speed of the river current?

Sagot :

Answer:9/2 km per hour

Step-by-step explanation:

equation,

6/9-x + 6/x=8/3

Upstream is flowing of the boat in the opposite direction of the stream. The speed of the river current is 4.5 km per hour.

Given-

Johnny and his father go fishing at 5:00 AM.

Total traveled by the Johnny and his father in upstream is 6 km.

The speed of the boat is 9 km/h.

What is upstream?

Upstream is flowing of the boat in the opposite direction of the stream.

Let x be the speed of the river current.

Time taken by the Johnny and his father to travel 6 km in upstream is ,

[tex]=\dfrac{6}{9-x}[/tex]

The time taken by the bottle to floats in the current river is,

[tex]=\dfrac{6}{x}[/tex]

As Johnny and his father start from 5:00 AM and the bottle reached to the point where Johnny and his father began their trip at 7:40 AM. Thus the total time is,

[tex]=7:40-5:00[/tex]

[tex]=2:40[/tex]

In hours,

[tex]=2\dfrac{40}{60}[/tex]

[tex]=\dfrac{8}{3}[/tex]

As the total time is equal to the sum of the Time taken by the Johnny and his father to travel 6 km in upstream and The time taken by the bottle to floats in the current river. Thus,

[tex]\dfrac{6}{9-x}+\dfrac{6}{x}=\dfrac{8}{3}[/tex]

[tex]\dfrac{6x+54-6x}{9x-x^2}= \dfrac{8}{3}[/tex]

[tex]\dfrac{27}{9x-x^2}= \dfrac{4}{3}[/tex]

[tex]x^2-9x+\dfrac{81}{4}=0[/tex]

On solving the above quadratic equation we get the positive value of the x is 4.5.

Thus the speed of the river current is 4.5 km per hour.

Learn more about the upstream here;

https://brainly.com/question/7567233

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