1. ## Find 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?

2. Hello, magentarita!

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?
We will use: .$\displaystyle \text{Time} \:=\:\frac{\text{Distance}}{\text{Speed}}$

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.
.

3. ## ok............

Originally Posted by Soroban
Hello, magentarita!

We will use: .$\displaystyle \text{Time} \:=\:\frac{\text{Distance}}{\text{Speed}}$

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.
.