Question

Productivity has been a concern for Jiang's moving company. When a moving job is too large, a one or two-person moving crew takes too long, and customers have been posting bad reviews. His moving crews can work at the following rates:

• Kevin can move a three-bedroom apartment in 5 hours.
• Quinton and Trey working together can do the same job in 2 hours.

Find the number of hours it would take for Kevin, Quinton, and Trey together to move a three-bedroom apartment.

a. 2.8 hours
b. 3.2 hours
c. 3.5 hours
d. 4.0 hours

Answer 1

To find the number of hours it would take for Kevin, Quinton, and Trey together to move a three-bedroom apartment, we can determine their combined rate of work. Kevin takes 5 hours, Quinton and Trey take 2 hours together. Their combined rate of work is 7/10 per hour, so it would take approximately 1.43 hours for all three to complete the job together.

Step-by-step explanation:

To find the number of hours it would take for Kevin, Quinton, and Trey together to move a three-bedroom apartment, we need to determine their combined rate of work. In this case, Kevin takes 5 hours to complete the job alone, and Quinton and Trey can do it in 2 hours together. We can use the formula: 1/Time taken = Rate of work.

So, Kevin's rate of work is 1/5 per hour, and Quinton and Trey's combined rate of work is 1/2 per hour. To find the combined rate of work for all three, we add their individual rates: 1/5 + 1/2 = 7/10.

Now, to find the time it would take for all three to complete the job together, we use the formula: Time taken = 1/Rate of work. Plugging in the combined rate of work of 7/10, we get: Time taken = 1/(7/10) = 10/7. Therefore, it would take approximately 1.43 hours for Kevin, Quinton, and Trey together to move a three-bedroom apartment.