Question: Kirby can embroider logos on a team’s sweatshirts in 5 hr. Traci, a new employee, needs 11 hr to complete the same job. Working together, how long will it take them to do the job?
1. **State the problem:** Kirby can complete the job in $5$ hours, and Traci can complete the same job in $11$ hours. We want to find how long it takes for both working together to complete the job.
2. **Formula used:** When two people work together, their combined work rate is the sum of their individual work rates. The time taken working together is the reciprocal of the combined rate.
3. **Calculate individual rates:**
- Kirby's rate = $\frac{1}{5}$ job per hour
- Traci's rate = $\frac{1}{11}$ job per hour
4. **Calculate combined rate:**
$$\text{Combined rate} = \frac{1}{5} + \frac{1}{11} = \frac{11}{55} + \frac{5}{55} = \frac{16}{55}$$ jobs per hour
5. **Calculate time working together:**
$$\text{Time} = \frac{1}{\text{Combined rate}} = \frac{1}{\frac{16}{55}} = \frac{55}{16}$$ hours
6. **Simplify the answer:**
$$\frac{55}{16} = 3 \frac{7}{16} \text{ hours}$$ or approximately $3.44$ hours.
**Final answer:** It will take them $\frac{55}{16}$ hours to do the job working together.