Question 306164
Lynn can paint room in 40 min .Jeff in 60 min. How long if both paint together?
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This is a typical shared work problem.
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Let t = time required when they work together (in minutes)
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Let the completed job = 1 (a painted room)
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Each person will paint a fraction of the room, the two fractions add up to 1
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{{{t/40}}} + {{{t/60}}} = 1
We can clear the fractions by multiplying 120, resulting in:
3t + 2t = 120
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5t = 120
t = {{{120/5}}}
t = 24 minutes working together
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We can prove that
{{{24/40}}} + {{{24/60}}} = 1
reduce the fractions
{{{6/10)}}} + {{{4/10}}} = 1
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This is a good method for most shared work problems.