During the first part of a trip, a canoeist travels 18 miles at a certain speed. the canoeist travels 4 miles on the second part of the trip at a speed 5 mph slower. the total time for the trip is 3 hrs. what was the speed on each part of the trip?

We can set it up like this, where s is the speed of the canoeist:



To make a common denominator between the fractions, we can multiply the whole equation by s(s-5):



If we rearrange this, we can turn it into a quadratic equation and factor:



Technically, either of these solutions would work when plugged into the original equation, but I would use the second solution because it's a little "neater."  We have the speed for the first part of the trip (9 mph); now we just need to subtract 5mph to get the speed for the second part of the trip.



The canoeist's speed on the first part of the trip was 9mph, and their speed on the second part was 4mph.