If Andrew can do a job in 8 hours and Bobby can do the same job in 12 hours, how long would it take the two men working together?

To solve how long it would take Andrew and Bobby to complete the job together, we can use the concept of work rates. 

Andrew's rate of work is:
\[
\text{Andrew's rate} = \frac{1}{8} \, \text{of the job per hour}.
\]

Bobby's rate of work is:
\[
\text{Bobby's rate} = \frac{1}{12} \, \text{of the job per hour}.
\]

When they work together, their combined rate is the sum of their individual rates:
\[
\text{Combined rate} = \frac{1}{8} + \frac{1}{12}.
\]

To add these fractions, we first need a common denominator. The least common denominator of 8 and 12 is 24, so we convert the fractions:
\[
\frac{1}{8} = \frac{3}{24}, \quad \frac{1}{12} = \frac{2}{24}.
\]

Now, add the two rates:
\[
\frac{3}{24} + \frac{2}{24} = \frac{5}{24}.
\]

This means that together, Andrew and Bobby complete \(\frac{5}{24

Learn how to calculate the time Andrew and Bobby take to complete a job together. Using work rates and adding fractions with a least common denominator, this problem is a great way to understand collaborative work. Suitable for students in Grades 6-8.

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