Question

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?

Answer 1

Answer:

13 km/h for 65 km

9 km/h for the next 27 km

Explanation:

Velocity of canoe =x km/h for 65 km

Velocity of canoe =x-4 km/h for 27 km after covering 65 km

Total time taken = 9 hours

So,

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

Solving this quadratic equation we get,

$x=\frac{15.5\pm \sqrt{240.25+130}}{2}=13\ or\ 2.5$

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