SOLUTION: Max and Joey both drove 100 miles from Monticello to Little Rock. Max drove 10 mph faster than Joey and got to Little Rock 20 minutes earlier. How fast did each drive?

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Question 284769: Max and Joey both drove 100 miles from Monticello to Little Rock. Max drove 10 mph faster than Joey and got to Little Rock 20 minutes earlier. How fast did each drive?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Max and Joey both drove 100 miles from Monticello to Little Rock. Max drove 10 mph faster than Joey and got to Little Rock 20 minutes earlier. How fast did each drive?
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Max DATA:
distance = 100 mi ; rate = x+10 mph ; time = 100/(x+10) hrs
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Joey DATA:
distance = 100 mi ; rate = x mph ; time = 100/x hrs
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Equation:
Joey time - Max time = 1/3 hr
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(100/x) - (100/(x+10)) = 1/3
Multiply thru by 3x(x+10) to get:
300(x+10) - 300x = x(x+10)
3000 = x^2 + 10x
Rearrange:
x^2 + 10x - 3000 = 0
Quadratic formula:
x = [-10 +- sqrt(100-4*-3000)]/2
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x = [-10 +- sqrt(12100)]/2
Positive solution:
x = [-10+110]/2
x = 50 mph (Joey's speed)
x+10 = 60 mph (Max's speed)
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Cheers,
Stan H.