Question 116938
1). Ryoma can paint their house 7 1/2 days, however Sakuno helped him and together they were able to do the painting in just 4 days. If Sakuno work alone how many days would it take to paint the whole house?
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Let x = S's time alone
Let the completed job = 1
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Each will do a fraction of the house:
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R's fraction + S's fraction = completed job
{{{4/7.5}}} + {{{4/x}}} = 1
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Multiply equation by 7.5x to get rid of the denominators:
7.5x*{{{4/7.5}}} + 7.5x*{{{4/x}}} = 7.5x(1)
Cancel out the denominators and you have;
4x + 7.5(4) = 7.5x
4x + 30 = 7.5x
30 = 7.5x - 4x
30 = 3.5x
x = 30/3.5
x = 8.57 days together or 8 days, 13.7 hrs
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2).A pipe can fill the pool in 6 hours. A small pipe can fill the pool in 8 hours. The pool will be empty within 12 hours. How long would it take to fill the pool if both filling pipe and draining pipe are both open?
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Let x = time required when working together
Let the full pool = 1
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Let filling be positive & draining be negative:
{{{x/6}}} + {{{x/8}}} - {{{x/12}}} = 1
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Multiply equation by 24 to get rid of the denominators
24*{{{x/6}}} + 24{{{x/8}}} - 24{{{x/12}}} = 24(1)
cancel out the denominators and you have:
4x + 3x - 2x = 24
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5x = 24
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x = 24/5
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x = 4.8 hr to fill the pool (or 4 hrs 48 min)