Final answer:
It will take 36 minutes for five spraying machines to paint a house if three machines can do it in 60 minutes. This is found by calculating the new combined work rate for the five machines and solving the equation for the time required. The correct option is a. 36
Step-by-step explanation:
If three spraying machines working together can finish painting a house in 60 minutes, we can calculate how long will it take for five machines of the same capacity to do the same job, using the concept of work rate.
The combined work rate of the three machines is 1 house per 60 minutes. We can represent this as 1/60. When we have five machines, their combined work rate would be (5/3) times that of the three machines, because there are (5/3) times as many machines.
The new combined work rate is (5/3) * (1/60). To find out how many minutes it takes for five machines to paint the house, we can set up the equation:
5 machines * X minutes = 1 job
(5/3) * (1/60) * X = 1
Now we solve for X:
X = 1 / ((5/3) * (1/60))
X = 3/5 * 60
X = 36 minutes
Therefore, it will take 36 minutes for five machines of the same capacity to paint the house. The correct answer is option a.