Question

During the first part of a trip a canoeist travels 55 miles at a certain speed the canoeist travels 15miles on the second part of the trip, 5 miles per hour slower. The total time for the trip is 4hours. What was the speed on each part of the trip.
This is what I have so far, then I am lost
t1= 55/r t2=15/r-5 =4
r (r-5) (55/r + 15/r-5) =4
55 (r-5) +15r=4r (r-5)
55r-275 + 15r=4r^2-20r
Now I am lost.

Answer 1

You are practically there!
Combine terms and rearrange to get into the form:

4r^2 -90r + 275 = 0

Use the quadratic formula to find r. There will be two answers. One of the answers is the result if the canoeist reverses direction (r-5 is negative).

Answer 2

r-5 being negative results in a negative t2 and so should be ignored.