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How do I solve the following problem?A boat travels 60 miles downstream in the same...

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catd1115 | Middle School Teacher | (Level 3) Assistant Educator

Posted April 12, 2012 at 1:25 PM via web

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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.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 12, 2012 at 1:55 PM (Answer #1)

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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.

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rch2012 | Student, Undergraduate | eNotes Newbie

Posted April 12, 2012 at 3:21 PM (Answer #2)

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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)

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