ruth can assemble a computer by herself in 55 minutes. erin does the same job in 60 minutes. how long will…

ruth can assemble a computer by herself in 55 minutes. erin does the same job in 60 minutes. how long will it take them to assemble a computer working together? write your answer as a fraction in lowest terms.

ruth can assemble a computer by herself in 55 minutes. erin does the same job in 60 minutes. how long will it take them to assemble a computer working together? write your answer as a fraction in lowest terms.

Answer

Explanation:

Step1: Identify individual work rates

Ruth's rate is $\frac{1}{55}$ computers/minute; Erin's rate is $\frac{1}{60}$ computers/minute.

Step2: Determine the combined work rate

$$\text{Combined Rate} = \frac{1}{55} + \frac{1}{60}$$

Step3: Find a common denominator

$$\frac{12}{660} + \frac{11}{660} = \frac{23}{660}$$

Step4: Calculate time by taking the reciprocal

$$\text{Time} = \frac{1}{\text{Combined Rate}} = \frac{660}{23}$$

Answer:

$\frac{660}{23}$ minutes