SOLUTION: A girl and her mother live 10 miles apart. They leave at the same time going the same direction. The mother drives 40 miles per hour. How fast must the girl drive to catch her m

Question 601489: A girl and her mother live 10 miles apart. They leave at the same time going the same direction. The mother drives 40 miles per hour. How fast must the girl drive to catch her mother in less than 30 minutes.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A girl and her mother live 10 miles apart. They leave at the same time going the same direction. The mother drives 40 miles per hour. How fast must the girl drive to catch her mother in less than 30 minutes.
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Mother DATA:
distance = x miles ; rate = 40 mph ; time = x/40 hrs.
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Daughter DATA:
distance = x + 10 miles ; time = x/40 hrs ; rate = (x+10)*(x/40) hrs
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Solve (x+10)(x/40) < 1/2 hr.
(x+10)(x) < 20 hrs
x^2 + 10x - 20 = 0
x = [-10 +- sqrt(100-4*-20)]/2
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x = [-10 +- sqrt(180)]/2
x = 6.76
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time = x/40 hrs = 0.169 hrs = 10.14 minutes
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Cheers,
Stan H.
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