SOLUTION: Jack and Jill fill pails of water everyday. On thursday, Jack worked for 2 hours and jill worked for 8 hours. Together they filled 30 pails of water. On Saturday Jack started early

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Question 566796: Jack and Jill fill pails of water everyday. On thursday, Jack worked for 2 hours and jill worked for 8 hours. Together they filled 30 pails of water. On Saturday Jack started early and worked for 2 hours before Jill could join him for 3 hours they filled 24 pails of water on saturday. How many pails will Jack and Jill fill if they work together for 7 hours?
Answer by stanbon(75887) About Me  (Show Source):
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Jack and Jill fill pails of water everyday.
On thursday, Jack worked for 2 hours and jill worked for 8 hours.
Together they filled 30 pails of water. On Saturday Jack started early and worked for 2 hours before Jill could join him for 3 hours they filled 24 pails of water on saturday.
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Let "a" be Jack's rate; Let "j" be Jill's rate.
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2a + 8j = 30
5a + 3j = 24
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Multiply 1st be 5 and 2nd by 2:
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10a + 40j = 150
10a + 6j = 48
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Subtract and solve for "j":
34j = 102
j = 3 pails per hour (Jill's rate)
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Solve for "a":
2a + 8j = 30
2a + 8*3 = 30
2a = 6
a = 3 pails per hour (Jack's rate)
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How many pails will Jack and Jill fill if they work together for 7 hours?
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7(3 + 3) = x
7*6 = x
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Ans: 42 pails
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