How do I solve the following problem?

A boat travels 60 miles downstream in the same time as it takes it to travel 40 miles upstream. The boat’s speed in still water is 20 miles/hour. Find the speed of the current.

### 2 Answers | Add Yours

You should come up with the notation for the speed of the boat such that: x miles/hour.

The speed of the boat upstream is x - 20 (the speed of boat in steel water).

The speed of the boat downstream is x + 20.

The problem provide the information that the boat travels 60 miles downstream in the same time it travels 40 miles upstream such that:

`60/(x+20) = 40/(x-20)`

`40(x+20) = 60(x-20)`

`2(x+20) = 3(x-20)`

You need to open brackets such that:

`2x + 40 = 3x - 60`

You need to move the terms that contains x to the left side such that:

`2x - 3x = -60 - 40`

`-x = -100 =gt x = 100`

**Hence, evaluating the speed of the current under given conditions yields `x = 100` miles/hour.**

If x is the speed of the current, then:

The speed of the boat downstream = 20 + x

The speed of the boat upstream = 20 - x

60 / (20 + x) = 40 / (20 - x)

x = 4 miles/hr (speed of the current)

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes