Kevin asked his trainee, Anna, to help call some of his clients to sell a newly-issued municipal bond. If he had to call all of the clients himself, it would take Kevin 6 hours to complete the job. If Anna alone were to call the clients, it would take her 9 hours. Working together, how long will it take Kevin and Anna to call all of the clients? a.) 3.0 hours b.) 3.6 hours c.) 2.8 hours d.) 4.5 hours

To figure out how long it will take Kevin and Anna to call all of the clients together, we first need to determine their individual rates of work. Kevin can complete the job in 6 hours, giving him a rate of \( \frac{1}{6} \) of the job per hour, while Anna's rate is \( \frac{1}{9} \) of the job per hour. Working together, their combined rate will be \( \frac{1}{6} + \frac{1}{9} \). Finding a common denominator (which is 18), we get: \[ \frac{3}{18} + \frac{2}{18} = \frac{5}{18} \] This means together, they can call \( \frac{5}{18} \) of the clients in one hour. To find the total time (T) taken to complete the job, we set up the equation: \[ \frac{5}{18} T = 1 \Rightarrow T = \frac{18}{5} = 3.6 \text{ hours}. \] Thus, the correct answer is **b.) 3.6 hours**. Did you know that teamwork can significantly enhance productivity? Just like in our scenario, Kevin and Anna's combined effort showcases the power of collaboration! When individuals pool their skills, jobs that seem daunting when tackled alone can become manageable—and even fun! Speaking of teamwork, this scenario is a classic in the realm of work rates, often popping up in various real-world situations. From construction teams to sales efforts like Kevin and Anna’s, the principles remain the same. Whether you’re dividing tasks among workers or planning a group study session, understanding how to calculate combined work rates is essential for efficiency!