7. It takes the same amount of time for Linda to paddle 10 miles up river as it does for her to paddle 18 miles down river. If the speed of the current is 2 mi/hr, how fast is she paddling?

We run through the steps for solving word problems. First define the unknown. After deciding what the problem is asking for we

let   x = how fast Linda is paddling.

When Linda is paddling downstream we would add the speed of the current to her paddling speed to get her actual velocity. When she is paddling upstream, we would take the speed of the current away from her paddling speed. Your author suggests that we make up a   d = rt   table.

We can fill in two columns if we use our unknown to express the rates. Once you have two columns in such a table filled in you can fill in the third by using the appropriate form of the   d = rt   equation. In this case the empty column is time, and

t = d/r

Using this we can fill in the third column.

Our information tells us that the time paddling upstream is the same as the time paddling downstream. This gives us

In this case, clearing denominators will amount to cross multiplying.

10(x + 2) = 18(x - 2)

Remove parentheses.

10x+ 20 = 18x- 36

Since there are more   x's   on the right than on the left, transpose   x   terms to the right and number terms to the left.

20 + 36 = 18x - 10x


56 = 8x


56/8 = x


x = 7


If Linda is paddling at 7 mi/hr then she would be moving 5 mi/hr upstream and 9 mi/hr downstream. At those rates, it would take her 2 hours to go 10 miles upstream and 2 hours to go 18 miles downstream, so it checks.

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