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bagirrra123 [75]
3 years ago
14

You are wakeboarding on a river. You travel 2 miles downstream to a marina for supplies, and then you travel 3 miles upstream to

a dock. The boat travels x miles per hour during the entire trip, and the river current is 3 miles per hour.
How long will the trip take when then speed of the boat is 18 miles per hour? Round to the nearest tenth minute.
Mathematics
1 answer:
Zielflug [23.3K]3 years ago
3 0

Let x represent the speed of of boat.

We have been given that the river current is 3 miles per hour.  

The speed of boat upstream will be x-3.

The speed of boat downstream would be x+3.

\text{Time}=\frac{\text{Distance}}{\text{Speed}}

We have been given that you travel 2 miles downstream to a marina for supplies, and then you travel 3 miles upstream to a dock.

We can represent this information in an equation as:

\text{Time}=\frac{2}{x+3}+\frac{3}{x-3}

Since the speed of the boat is 18 miles per hour, so we will substitute x=18 in above equation and solve for time.

\text{Time}=\frac{2}{18+3}+\frac{3}{18-3}

\text{Time}=\frac{2}{21}+\frac{3}{15}

\text{Time}=\frac{2}{21}+\frac{1}{5}

\text{Time}=\frac{2\cdot 5}{21\cdot 5}+\frac{1\cdot 21}{5\cdot 21}

\text{Time}=\frac{10}{105}+\frac{21}{105}

\text{Time}=\frac{31}{105}

\text{Time}=0.295238095

Since time is in hours, so let us convert our given time in minutes.

1 hour = 60 minutes.

\text{Time}=0.295238095\times 60\text{ minutes}

\text{Time}=17.7142857\text{ minutes}

Rounding to nearest tenth of minute.

\text{Time}\approx 17.7\text{ minutes}

Therefore, it will take approximately 17.7 minutes for the boat to take the trip.

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