Problema Solution
During the first part of a trip, a canoeist travels 67 miles at a certain speed. The canoeist travesl 13 miles on the second part of the trip at a speed of 5 mph slower. The total time of trip is 2 hrs. What was the speed on each part of the trip?
Answer provided by our tutors
We know that time is distance/speed
t=x/sSpeed of first part is s, speed of second part is 5 mph slower, so s-5
2=(67/s)+(13/(s-5))
Rearrange in to quadratic form
2 = (67(s-5)+13s)/(s^2 - 5s)
0 = 2s2-90s+335
USE QUADRATIC FORMULA
s=(-b ± sqrt(b2-4ac))/2a
a=2
b = -90
c=335
We get two answers: s = 40.91 and s=4.09
The second answer is impossible since we need to be able to get a positive value for s-5
So the speed for the first part of the trip is s=40.91 mph
and the speed for the second part of the trip is s-5 = 35.91 mph