Question

Please help me with this question.

Answer 1

103 minutes or, equivalently, 1 hour 43 minutes

Explanation:

These types of -problems are referred to as work rate problems or sometimes work rate time problems

To solve these types of problems find the rate of work of each individual and add up the rates to find the combined rate for all individuals

Let's use x for Mr Cole and y for Mrs. Cole

The important piece of info here is that all the bedrooms are the same size so the work rate for any bedroom is the same for x and the same for y

y can paint a bedroom in 4 hours.
So rate of work for y = 1/4 bedroom per hour

x can paint the bedroom in 3 hours
So rate of work for x = 1/4 bedroom per hour

Let t be the time in hours taken for both of them to paint a bedroom
Each of them will work t hours irrespective of their rate of work

For x the work done is
`(1)/(3)t = (t)/(3)` of the bedroom

For y the work done is
`(1)/(4)t = (t)/(4)` of the bedroom

Together in t hours they finish 100% of the bedroom; ie 1

So

`(t)/(3) + (t)/(4) =1\\\\(4t + 3t)/(12) = 1\\\\(7t)/(12) = 1\\\\t = (12)/(7) \;hours\\\\\text{In minutes this would be:\\}\\\\(12)/(7) \cdot 60 = 102.85 \;\rm{minutes}}`

Rounded to the nearest minute that would be 103 minutes or

`(103)/(60) \;\rm{ hours}`

The quotient is 1 and the remainder is 43 when you divide 103 by 60

That means it takes 1 hour and 43 minutes for both of them working together to paint the third bedroom