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.