SOLUTION: solve the following special system: Micah walks on a treadmill at 4 miles per hour. He has walked 2 miles when Luke starts running at 6 miles per hour on the treadmill next to him

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Question 379235: solve the following special system:
Micah walks on a treadmill at 4 miles per hour. He has walked 2 miles when Luke starts running at 6 miles per hour on the treadmill next to him. If their rates continue, will Luke's distance ever equal Michah's distance. Explain.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Micah is 2 miles ahead.
Luke gains on him at 2 mph (6-4)
2/2 = 1 hour

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Micah walks on a treadmill at 4 miles per hour. He has walked 2 miles when Luke starts running at 6 miles per hour on the treadmill next to him. If their rates continue, will Luke's distance ever equal Michah's distance. Explain.
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Note: Micah's time to run 2 miles at 4 mph = 1/2 hour.
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Micah DATA:
rate = 4 mph ; time = x+(1/2) hrs ; distance = 4(x+(1/2)) = 4x+2 miles
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Luke DATA:
rate = 6 mph ; time = x hrs ; distance = 6x miles
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Equation:
distance = distance
4x+2 = 6x
2x = 2
x = 1 hr.
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Distances will be equal after Luke has run for one hour.
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Cheers,
Stan H.
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