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=(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=(d)/(S) \\ (12)/((x+2))=(8)/((x-2)) \\ (x+2)8=12(x-2) \\ 8x+16=12x-24 \\ 8x-12x=-24-16 \\ -4x=-40 \\ (-4x)/(-4)=-(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