SOLUTION: George a race-walker, is on one end of a 6 mile track. John a average walker is on the other end of the track. The two start walking towards each other and meet in 1/2 hour. If Geo

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Question 450282: George a race-walker, is on one end of a 6 mile track. John a average walker is on the other end of the track. The two start walking towards each other and meet in 1/2 hour. If George's average speed exceeds John's by 6 mph, find the speed of both walkers. How do I set up and solve the equation?
This is what I came up with: r+6= rate of George
1/2r + 1/2(r+6)=6 John=3 mph
1/2r + 1/2r + 3=6 George=9 mph
r + 3=6
r+3-3=6-3
r=3
3+6=9
Found 2 solutions by jorel1380, solver91311:
Answer by jorel1380(3719) (Show Source):
You can put this solution on YOUR website!
1/2x+1/2(x+6)=6
1/2x+1/2x+3=6
x=3
John walks 3mph, George walks 9mph
1/2x3+1/2x9=3/2+9/2=12/2=6..

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Nothing whatsoever wrong about the way you did the problem. Actually, this is a two-by-two linear system problem that lends itself neatly to solution by the Substitution method. You simply skipped the step of writing the quantity equation that relates the two speeds, solving that equation for one of the speeds, and then substituting the expression into your second equation. But there is nothing wrong with that approach when the relationships are this simple.

John

My calculator said it, I believe it, that settles it