Question

9. A boat travels 12 miles with the current in the same time it travels 8 miles against thecurrent. If the speed of the current is 2 mph, find the speed of the boat.

Answer 1

$10\:mph$

1) In this kind of question, we're going to deal with a ratio:

$Speed=\frac{t}{d}$

2) So, now let's gather the data:

Upstream: 8 miles

Downstream: 12 miles

Speed of the current: 2mph

Boat speed: x

So we can set the following expression:

$\begin{gathered} t=\frac{d}{S} \\ \frac{12}{(x+2)}=\frac{8}{(x-2)} \\ (x+2)8=12(x-2) \\ 8x+16=12x-24 \\ 8x-12x=-24-16 \\ -4x=-40 \\ \frac{-4x}{-4}=-\frac{40}{-4} \\ x=10 \end{gathered}$

Note that we actually equate both rational expressions for the boat against the current and the boat with the current.

Thus, the boat speed is 10 mph