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A tourist boat is used for sightseeing in a nearby river. The boat travels 2.4 miles downstream and in the same amount of time, it travels 1.8 miles upstream. If the boat travels at an average speed of 21 miles per hour in the still water, find the current of the river. (SHOW WORK)

Respuesta :

frika

Answer:

3 miles per hour

Step-by-step explanation:

Let x miles per hour be the current of the river.

1. The boat travels 2.4 miles downstream with the speed of (21+x) miles per hour. It takes him

[tex]\dfrac{2.4}{21+x}\ hours.[/tex]

2. The boat travels 1.8 miles upstream with the speed of (21-x) miles per hour. It takes him

[tex]\dfrac{1.8}{21-x}\ hours.[/tex]

3. The time is the same, so

[tex]\dfrac{2.4}{21+x}=\dfrac{1.8}{21-x}[/tex]

Cross multiply:

[tex]2.4(21-x)=1.8(21+x)[/tex]

Multiply it by 10:

[tex]24(21-x)=18(21+x)[/tex]

Divide it by 6:

[tex]4(21-x)=3(21+x)\\ \\84-4x=63+3x\\ \\84-63=3x+4x\\ \\7x=21\\ \\x=3\ mph[/tex]

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