Question 55990
John and Fred must mow the lawn before they can go swimming. 
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By themselves, John would take 30 minutes and Fred would take 45 minutes. How long would it take to mow the lawn with both working together?
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Let t = time in minutes working together
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During this time we can say John would do t/30 of the job and
Fred would do t/45 of the job
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Let the completed job = 1, giving us an easy equation:
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{{{t/30}}} + {{{t/45}}} = 1
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We can get rid of the denominators by mult by 90, then we have:
3t + 2t = 90
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5t = 90
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t = 90/5
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t = 18 min when they work together
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Check our solution: {{{18/30}}} + {{{18/45}}}  =  {{{3/5}}} + {{{2/5}}} = 1