SOLUTION: 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

Question 1174986: 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 by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Given that his speed on level ground is the average of his uphill and downhill speeds, let the three speeds be

x+y downhill
x on level ground
x-y uphill

2 hours uphill and 3 hours on level ground covered 115 km:
2(x-y)+3(x) = 115

2 hours downhill and 3 hours on level ground covered 135 km:
2(x+y)+3(x) = 135

Solve the pair of equations using basic algebra.

2x-2y+3x = 115
5x-2y = 115

2x+2y+3x = 135
5x+2y = 135

Comparing the two equations (i.e., subtracting one from the other)....

4x = 20
x = 5

Plug x=5 into one of the equations to solve for y; then use your x and y values to find the three speeds.

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