During the first part of a trip, a canoeist covered 65 km at a certain speed. He then traveled 27 km at a speed that was 4 km/h slower. If the total time for the trip was 8 hr, what was the speed on each part of the trip?

[tex]\frac{65}{x}+\frac{27}{x-4}=8\\\Rightarrow \frac{65(x-4)+27x}{x^2-4x}=8\\\Rightarrow \frac{92x-260}{8}=x^2-4x\\\Rightarrow 11.5x-32.5=x^2-4x\\\Rightarrow x^2-15.5x+32.5=0[/tex]

Solving this quadratic equation we get,

[tex]x=\frac{15.5\pm \sqrt{240.25+130}}{2}=13\ or\ 2.5[/tex]

Speed cannot be 2.5 as the speed will become negative for the 27 km stretch.

So, velocity of canoe is 13 km/h for 65 km and 9 km/h for the next 27 km

During the first part of a​ trip, a canoeist covered 65 km at a certain speed. He then traveled 27 km at a speed that was 4 ​km/h slower. If the total time for the trip was 8 ​hr, what was the speed on each part of the​ trip?

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During the first part of a trip, a canoeist covered 65 km at a certain speed. He then traveled 27 km at a speed that was 4 km/h slower. If the total time for the trip was 8 hr, what was the speed on each part of the trip?