Final answer:
To find how long it will take Frank and Elise to clean the garage together, we can use their individual rates of work. Frank can clean the garage in 3 hours and Elise takes 4 hours. By finding their combined rate of work, we can determine the time it will take them to clean the entire garage and we get approximately 12/7 hours .
Step-by-step explanation:
To find out how long it will take Frank and Elise to clean the garage together, we can use the concept of work. However, before we can do that, we need to find their individual rates of work. Frank can clean the garage in 3 hours, so his rate of work is 1/3 of the garage per hour. Elise, on the other hand, takes 4 hours to clean the garage, so her rate of work is 1/4 of the garage per hour. To find their combined rate of work, we can add their individual rates: 1/3 + 1/4 = 7/12. This means that together, they can clean 7/12 of the garage per hour. To find how long it will take them to clean the entire garage, we can divide the work (1 garage) by their combined rate of work (7/12 garage per hour). This gives us 1 / (7/12) = 12/7. So it will take them approximately 12/7 hours or 1 and 5/7 hours to clean the garage together.