Question

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.

Answer 1

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.