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Question 644246: If a girl works for 8 min. and her brother works for 15 min, they can wash the front windows of their house. Also, if the girl works for 12 min and her brother works for 10 min, they can wash the same windows. How long will it take each person alone to wash the windows? (Hint: If it takes t minutes for a person to do a job alone, then in 1 min, the person can do 1/t of the job).
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If a girl works for 8 min. and her brother works for 15 min, they can wash the front windows of their house. Also, if the girl works for 12 min and her brother works for 10 min, they can wash the same windows. How long will it take each person alone to wash the windows? (Hint: If it takes t minutes for a person to do a job alone, then in 1 min, the person can do 1/t of the job).
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Let the girl's rate be "g" and the brother's rate be "b".
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Equation:
8g + 15b = 1 job
12g+ 10b = 1 job
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80g + 150b = 10
180g + 150b = 15
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100g = 5
g = 1/20 (girl's rate)
1/g = 20 minutes (time for the girl to do the job alone)
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Solve for "b":
80(1/20) + 150b = 10
150b = 6
b = 1/25
1/b = 25 minutes (time for the brother to do the job alone)
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Cheers,
Stan H.
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