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skelet666 [1.2K]
3 years ago
14

A boat can travel 12 km down the river in the same time it can go 4 km up the river. If the current in the river is 2 km per hou

r, how fast can the boat travel in still water?
I know the answer is "4 km per hour" from the book but I don't know how to show the work so please help me. thank you
Mathematics
1 answer:
blondinia [14]3 years ago
4 0

Answer:

The speed of the boat in still water is 4 km per hour

Step-by-step explanation:

Let

s ---> the total speed of the boat in km/h

x ----> the speed of the boat in still water in km/h

t ----> the time in hours

d ---> the distance in km

Remember that the speed is equal to the distance divided by the time

so

The time is the distance divided by the speed

so

<em>Down the river</em>

t=\frac{d}{s}

we have

d=12\ km\\s=(x+2)\ km/h

Remember that the speed of the boat down the river is equal to the speed of the boat in still water plus the speed of the current

substitute

t=\frac{12}{x+2} ----> equation A

<em>Up the river</em>

t=\frac{d}{s}

we have

d=4\ km\\s=(x-2)\ km/h

Remember that the speed of the boat up the river is equal to the speed of the boat in still water minus the speed of the current

substitute

t=\frac{4}{x-2} ----> equation B

Equate equation A and equation B

\frac{12}{x+2}=\frac{4}{x-2}

solve for x

Multiply in cross

12(x-2)=4(x+2)\\12x-24=4x+8\\12x-4x=24+8\\8x=32\\x=4\ km/h

therefore

The speed of the boat in still water is 4 km per hour

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