During the first part of a trip, a canoeist travels 37 miles at a certain speed. The canoeist travels 7 miles on the second part or the trip at a speed 5 mph slower. The total time for the trip is 4 hours. What is the speed on each part of the trip?

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- Nov 25th 2008, 10:16 PMmagentaritaFind the Speed
During the first part of a trip, a canoeist travels 37 miles at a certain speed. The canoeist travels 7 miles on the second part or the trip at a speed 5 mph slower. The total time for the trip is 4 hours. What is the speed on each part of the trip?

- Nov 26th 2008, 07:08 AMSoroban
Hello, magentarita!

Quote:

During the first part of a trip, a canoeist travels 37 miles at a certain speed.

The canoeist travels 7 miles on the second part or the trip at a speed 5 mph slower.

The total time for the trip is 4 hours.

What is the speed on each part of the trip?

Let $\displaystyle r$ = speed on the first part.

Then $\displaystyle r - 5$ = speed on the second part.

He went 37 miles at $\displaystyle r$ mph.

. . This took: .$\displaystyle \frac{37}{r}$ hours.

He went 7 miles at $\displaystyle r-5$ mph.

. . This took: .$\displaystyle \frac{7}{r-5}$ hours.

His total time was 4 hours: . $\displaystyle \frac{37}{r} + \frac{7}{r-5} \:=\:4$

Now solve for $\displaystyle r$ . . .

Warning: We get a quadratic that doesn't factor.

. . . . . . .Use the Quadratic Formula and approximate the answer.

. - Nov 28th 2008, 05:09 AMmagentaritaok............