Question 584026: A family plans to drive 2000 miles in 33 hours. The father will drive half of the distance, and the mother and son will share equally the remaining distance.
In general, the father drives the fastest, the mother drives 10 mile per hour slower than the father, and the son's rate is halfway between the mother's and father's rates.
find the rates for each of the drivers.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A family plans to drive 2000 miles in 33 hours. The father will drive half of the distance, and the mother and son will share equally the remaining distance.
In general, the father drives the fastest, the mother drives 10 mile per hour slower than the father, and the son's rate is halfway between the mother's and father's rates.
find the rates for each of the drivers.
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Let Mother's rate be x mph
Then Father's rate is 2x mph
And son's rate = (3/2)x
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Father's time: 1000/2x = 500/x hrs
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Mother's time: 250/x hrs
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Son's time: 250/(3/2)x = (500/(3x)) hrs
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Solve for "x":
(500/x) + (250/x) + 500/(3x) = 33
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Multiply thru by 3x to get:
1500 + 750 + 500 = 99x
2750 = 99x
x = 2750/99
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x = 27.78 mph (Mother's rate)
2x = 55.56 mph (Father's rate)
(3/2)x = 41.67 mph (Son's rate)
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cheers,
Stan H.
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