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Question 523482: working alone jennifer can pick forty bushels of apples in 12 hours . tosakan can pick the same amount in 10 hours .how long would it take them if they worked together
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Work problems like this are solved by using fractions.
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Jennifer can pick 40 bushels of apples in 12 hours.
We can define "picking 40 bushels of apples" as 1 whole job.
She does 1/12 of the job per hour.
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Tosakan can do the job in 10 hours.
She does 1/10 of the job per hour.
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x = number of hours working together to do the job
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(1/12 + 1/10)*x hours = 1 whole job
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(1/12 + 1/10)*x = 1
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22/120*x = 1
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22x = 120
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x = 120/22 = 60/11
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60/11 = 5 5/11 hours
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5/11 hr * 60 min/hr = 300/11 = 27.27272727272727 or about 27.3 min.
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Working together they can do the job in 5 5/11 hr or about 5 hr and 27.3 min.
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Always check your solution to see if it is the answer.
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How many bushels does Jennifer pick in 60/11 hr?
She picks 40 in 12 hr, so she picks 10/3 bushels per hr.
60/11 hr * 10/3 bushels/hr = 600/33 = 200/11 = 18.18181818181818 bushels
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How many bushels does Tosakan pick in 60/11 hr?
She picks 40 in 10 hr, so she picks 4 bushels per hr.
60/11 hr * 4 bushels/hr = 240/11 = 21.81818181818182 bushels
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Answer: They can pick 40 bushels in 5 5/11 hr working together.
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Done.
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