Question 123887
Manuel arranges all the seats in the auditoriums in 7 hours, while Pedro takes only 5 hours. How long will it take if they work together? 
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Let t = time required, when they work together
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Let the completed job = 1
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A simple equation
M's fraction of the job + P's fraction of the job = 1 (completed job)
:
{{{t/7}}} + {{{t/5}}} = 1
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Multiply equation by a multiple of 5 and 7 to get rid of the denominators (35)
35*{{{t/7}}} + 35*{{{t/5}}} = 35(1)
cancel out the denominators and you have:
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5t + 7t = 35
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12t = 35
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t = {{{35/12}}}
t = 2.917 hrs working together
;
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Check our solution:
{{{2.917/7}}} + {{{2.917/5}}} = 1
 .4167 + .5834 = 1.000; confirms our solution