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Rachel can finish the job in 5 hours, while Carl can finish the same job in 8 hours.

How long will it take them to finish the job together?

User Dmind
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1 Answer

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Final answer:

To find out how long Rachel and Carl would take to complete a job together, we add their rates of work to get a combined rate and then find the reciprocal of this rate, resulting in approximately 3 hours and 5 minutes.

Step-by-step explanation:

Calculating Time Taken for Rachel and Carl to Finish a Job Together

When Rachel and Carl work together, the total time taken to finish a job is calculated by adding the rates at which they complete the job individually. Rachel completes the job in 5 hours, so her rate is 1 job per 5 hours, or 1/5 job per hour. Carl completes the job in 8 hours, so his rate is 1 job per 8 hours, or 1/8 job per hour.

When combined, their total rate is the sum of their individual rates (1/5 + 1/8). This sum represents how much of the job they complete together in one hour. To find the sum of the fractions, we need a common denominator, which is 40 in this case:

Total rate = 1/5 + 1/8 = 8/40 + 5/40 = 13/40 job per hour

To calculate the time it takes for them to complete the job together, we take the reciprocal of this total rate. The reciprocal of 13/40 is 40/13 hours, which is approximately 3.08 hours or 3 hours and 5 minutes. Therefore, it would take Rachel and Carl approximately 3 hours and 5 minutes to complete the job together.

User Sebastian Wagner
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