Answer the following:

Question

Serge’s outgoing 115-kilometer bike involved riding uphill for 2 hours and on level ground for 3 hours. On the return trip, on a different 135-kilometer trail, he rode downhill for 2 hours and on level ground for 3 hours. Determine Serge’s three speeds if his speed on level ground is the average of his uphill and downhill speeds.

Answer 1

let x = speed on level ground, let g = effect on speed of gravity

2(x+g) + 3x = 135

2x + 2g + 3x = 135

5x + 2g = 135

2(x-g) + 3x = 115

2x -2g + 3x = 115

5x -2g = 115

add the two equations

5x + 2g = 135

5x - 2 g = 115

10x = 250

x = 25 km/hr on level ground

subtract the two equations to solve for g

4g = 20

g = 5

x+5 = 30 km/hr downhill

x-5 = 20 km/hr uphill