jose can complete the job in a hours, and Maria can complete the job in b hours. How long does it take them to complete the job when they work together? I need a formula
Jose's rate = job/a
Maria's rate = job/b
combined rate = job/a + job/b
= job(a+b)/(ab)
combined time = job/combined rate
= job/[job(a+b)/(ab)]
= ab/(a+b)
To find the time it takes for Jose and Maria to complete the job when they work together, we can use the formula:
1 / (1/a + 1/b)
In this formula, "a" represents the number of hours Jose takes to complete the job, and "b" represents the number of hours Maria takes to complete the job.
By substituting the given values of a and b into the formula, we can calculate the answer:
1 / (1/a + 1/b) = 1 / (1/5 + 1/3)
Let's simplify this calculation step-by-step:
First, we need to find the sum of the fractions 1/5 and 1/3:
1/5 + 1/3 = (3/15) + (5/15) = 8/15
Then, we can substitute this value back into the formula:
1 / (8/15) = 15/8
Therefore, when Jose and Maria work together, it will take them 15/8 hours to complete the job.