machine a, working alone at its constant rate, produces x pounds of peanut butter in 12 minutes. machine b, working alone at its constant rate, produces x pounds of peanut butter in 18 minutes. how many minutes will it take machines a and b, working simultaneously at their respective constant rates, to produce x pounds of peanut butter?

Time and work defines the way how the particular work is done in the given time. It gives an exact relationship between the work and the number of days required to complete it.

Calculation of the total time taken by the machines A and B working together

Given that Machine A completes the entire job in 12 minutes.

So, machine A completes 1/12 of the job in one minute.

Machine B takes 18 minutes to complete the entire job.

So, machine B completes 1/18 of the job in one minute

When we combine their work, they will complete (1 / 12 + 1 / 18) job in one minute i.e. (3 + 2) / 36 = 5/36 job in one minute —---- 1

To find the time taketaken by them to produce x amount of peanut butter, we will reciprocate the result obtained in equation 1

i.e. 36 / 5 minutes to complete the entire job

i.e. 7.2 minutes

Hence, the time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.

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