40 POINTS 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.

Type the correct answer in the box. Use numerals instead of words.

It would take the three movers __ minutes to move a three-bedroom apartment.

They can complete the job in 1.43 hours.

Step-by-step explanation:

Let's define:

"moving a three-bedroom" as "one job"

We know that Kevin can complete one job in 5 hours, then he works at the rate:

K = (1 job)/(5 hours) = (1/5) job per hour.

Now if Q is the rate at which Quinton works and T is the rate at which Trey works, their combined rate is (Q + T), and they can complete the job in 2 hours, then:

(Q + T) = (1 job)/(2 hours) = (1/2) job per hour.

When Kevin, Quinton, and Trey wor togheter, the combined rate is:

(K + Q + T)

And we know that:

(Q + T)  = (1/2) job per hour.

K =  (1/5) job per hour.

If we replace these in the above sum we get:

(K + Q + T) =  (1/5) job per hour + (1/2) job per hour

                 = (1/5 + 1/2) job per hour

                 = (2/10 + 5/10) job per hour

                 = (7/10) job per hour.

Then they need to work for T hours in order to complete 1 job, we have the equation:

[ (7/10) job/hour]*T = 1 job

T = ( 1 job)/(7/10) job/hour = 10/7 hours = 1.43 hours.

they can complete the job in 1.43 hours.

85.7 minutes

Step-by-step explanation:

Explanation:

Use this formula:

1 apartment/x hours =  1/x of an apartment.

Calculate the combined rate of the moving crews:

1 apartment/ 5 hours + 1 apartment/ 2 hours  = 1 apartment/ x hours.

Find a common denominator:

2+5 / 10 = 1 / x

7 / 10 = 1 / x

x = 10 / 7

1 hour = 60 minutes

So, the time it would take this three-person moving crew is 10 / 7 × 60 = 85.7 minutes.

Courtesy of edmentum :)

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