Question

during the first part of a trip a canoeist travels 100 miles at a certain speed. The canoeist travels 23 miles on the second part of the trip at a speed of 5 mph slower the total time for the trip is 3 hours what was the speed on each part of the trip

Answer 1

ready to do this one, together?

Answer 2

nope i dont now how

Answer 3

okay well i can show you , but we have to work together, okay

Answer 4

r t = d, t=d/r

The time for the first part is 100 divided by r. The time for the second part is 23/(r-5). The sum of the times is 3 hours.

Solve the following for r:\[\frac{100}{r}+\frac{23}{r-5}=3\]\[\left\{r=\frac{1}{3} \left(69-\sqrt{3261}\right),r=\frac{1}{3} \left(69+\sqrt{3261}\right)\right\} \]or\[\{r=3.96494,r=42.0351\} \]r = 3.9 is too small because the denominator of the second fraction of the equation goes negative. At 42+ miles per hour, this canoe is definitely not human powered.
The speeds are 42.0351 mph and 37.0351 mph for the first part and the second part of the trip respectively.

The times for each trip part is 2.37897 and 0.62103 hours respectively and the sum of these times is 3.0 hours to 5 digits in the decimal fraction.\[42.0351\text{ mph}*2.37897\text{ hours}=100.\text{ miles} \]\[37.0351\text{ mph}*0.621033\text{ hours}=23.\text{ miles} \]