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Josephine can correct her students’ test papers in 7 hours, but if her teacher’s assistant helps, it would take them 5 hours. How long, in hours and minutes, would it take the assistant to do it alone. Write in mixed units

User Azfar Niaz
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1 Answer

14 votes
14 votes

Answer: it will take the assistant to do it alone 17 1/2 hours

Step-by-step explanation:

Let x represent the number of hours it will take the assistant to do it alone. This means that the unit work rate per hour is 1/x

If Josephine can correct her students’ test papers in 7 hours, it means that the unit work rate per hour is 1/7

If both of them can do the job in 5 hours, it means that their combined unit rate is 1/5

Since the rates are independent, it means that

1/x + 1/7 = 1/5

The lowest common multiple of the denominators is 35x. Multiplying through by 35x, we have

35 + 5x = 7x

7x - 5x = 35

2x = 35

x = 35/2 = 17/2

it will take the assistant to do it alone 17 1/2 hours

User Lukstei
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