Problema Solution
During the first part of a trip, a canoeist travels 63miles at a certain speed. The canoeist travels 24 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip?
Answer provided by our tutors
Let V be the canoeist's speed on the first part of the trip.
Time = distance / speed
So T1 = time on first part = 63 / V
and T2 = time on 2nd part = 6 / (V-5)
T1 + T2 = 5
So 63/V + 6/(V-5) = 5
This is the equation you must solve for V.
Common denominator is V*(V-5); multiply both sides by it:
63(V-5) + 6V = 5V(V-5)
expand:
63V - 315 + 6V = 5V^2 - 25V
collect terms:
5V^2 - 94V + 315 = 0
Solve using the quadratic formula. I used a website calculator here:
https://www.math.com/students/calculators/source/quadratic.htm
One root is negative and should be discarded.
The other root is V = 14.4+
So 14.4 mph on the first part, 9.4 mph on 2nd part. Plug back in to the problem -- it checks -- approximately.
You might be required to give an exact formula in terms of radicals, in which case forget the quadratic calculator & work it out exactly.