Colin and Rob are travelling 240 km from home to a campground on Prince Edward Island on separate motorcycles. While they both make the trip, Colin's speed was 20 km/h less than Rob's and it took him 1 hour longer to complete the trip. Determine each boy's average speed.

Answer 1

Let R be the speed in km/h of Rob's motorcycle.
Then Colin's motorcycle was traveling at a speed of R - 20 km/h.
We know that the time Colin traveled was equal to the time Rob traveled plus 1 hour, or T = T+1.
So, 240 km = T * R distance for Rob's motorcycle
And 240 km = (T + 1) * (R - 20) distance for Colin's motorcycle
So, 240 / R = T and 240 / (R - 20) = T + 1
Multiplying both sides of the second equation by R - 20, we get 240R/(R - 20) = T + 1
Combining the equations for T, we get 240 / R = 240R/(R - 20) - 1 or 1/R = R/(R - 20) - 1/240
Multiplying both sides by R(R - 20)(240), we get (R - 20)(240) = 240*R - R(R - 20)
Opening the brackets, we get 240R - 4800 = 240R - R^2 + 20R
Moving the terms to one side, we get 0 = R^2 + 20R - 4800
Dividing the whole equation by 20, we get R^2 + R - 240 = 0
Factoring the quadratic equation, we get (R - 12)(R + 20) = 0
Therefore, either R = 12 or R = -20
As the speed cannot be negative, the speed of Rob's motorcycle is 12 km/h.
Therefore, Colin's speed is R - 20 = 12 - 20 = -8 km/h, which is impossible.
Therefore, Colin's speed is 12 - 20 = 2 km/h.
So, the average speed of Rob's motorcycle is R = 12 km/h and the average speed of Colin's motorcycle is 2 km/h. Answer: \boxed{12, 2}.