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...

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.

Expert Answers
sciencesolve eNotes educator| Certified Educator

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.

rch2012 | Student

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)