SOLUTION: Jason and Marie both travel 900 miles. Jason drove at an average speed of 10 miles per hour faster than Marie and made the trip in one hour less time. Find the average speeds of bo

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Question 390833: Jason and Marie both travel 900 miles. Jason drove at an average speed of 10 miles per hour faster than Marie and made the trip in one hour less time. Find the average speeds of both cars.
Jason's speed = ?mph
Marie's speed = ?mph
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Jason and Marie both travel 900 miles. Jason drove at an average speed of 10 miles per hour faster than Marie and made the trip in one hour less time. Find the average speeds of both cars.
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Jason DATA:
distance = 900 miles ; rate = x+10 mph ; time = 900/(x+10) hrs
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Marie DATA:
distance = 900 miles ; rate = x mph ; time = 900/x hrs
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Equation:
time - time = 1 hr
900/x - 900/(x+10) = 1 hr
900x+9000 - 900x = x(x+10)
x^2+10x-9000 = 0
(x+100)(x-90) = 0
Positive solution:
x = 90 mph (Marie's speed)
x+10 = 100 mph (Jason's speed)
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Cheers,
Stan H.
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Jason's speed = ?mph
Marie's speed = ?mph