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Ben can prepare a company report in 3 hours. Shane can prepare a report in 4.2 hours.How long will it take them, working together, to prepare eight company reports?It will take hours for them to prepare eight company reports.(Simplify your answer. Round to the nearest hour as needed.)

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Ben can prepare a company report in 3 hours. This means that the time rate with which Ben can prepare the report is 1/3

Shane can prepare a report in 4.2 hours. This means that the time rate with which Shane can prepare the report is 1/4.2

Let the time at which they would prepare the report if they work simultaneaosly be t. Then, their combined time rate is 1/t

Thus, it means that

1/3 + 1/4.2 = 1/t

(4.2 + 3)/12.6 = 1/t

7.2/12.6 = 1/t

By cross multiplying, it becomes

7.2t = 12.6

t = 12.6/7.2

t = 1.75

If they work together, they will prepare a report in 1.75 hours. Thus, the time needed to prepare eight reports is

1.75 * 8 = 14 hours

It will take them 14 hours to prepare 8 reports

User Dominik Reinert
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