During the first part of a trip, a canoeist travels 83 miles at a certain speed. The canoeist travels 19 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2 hours. What was the speed on each part of the trip?
(working with the quadratic formula).

Question

jim_thompson5910 · Answer

$$\frac{83}{x}+\frac{19}{x-5}=2$$


$$83(x-5)+19x=2x(x-5)$$


$$83x-415+19x=2x^2-10x$$


$$102x-415=2x^2-10x$$


$$0=2x^2-10x-102x+415$$


$$0=2x^2-112x+415$$


Now use the quadratic formula (see attached) to get


$$x=\frac{56+\sqrt{2306}}{2} \ \textrm{or} \ x=\frac{56-\sqrt{2306}}{2}$$


and using a calculator, they approximate to 


$$x=52.0104 \ \textrm{or} \ x=3.9896$$


Since x=3.9869 is too small, this means that the only answer is x=52.0104


So the speed on the first part of the trip was roughly 52.0104 mph


and the speed on the second part was roughly 52.0104-5 = 47.0104 mph