Answer: 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.
