Work math problem?

Question

Roger can paint a room in 6 hrs, Chris can paint the room in 8 hrs. If they begin together and Chris takes a 1 hr break determine the amount of time in hrs and minutes that it will take the room to be painted.

no clue as to how to do the problem

Answer 1

Roger can paint 1/6 room per hour
Chris can paint 1/8 room per hour
Together they can paint 1/6 + 1/8 room per hour
1/6 + 1/8 = 14/48 = 7/24

But Chris take a one-hour break. Let's put that at the beginning to simplify the problem. It could occur anywhere and the answer would be the same.

So, 1/6 of the room is painted in the first hour while Chris is on break. That leaves 5/6 of the room to paint.

Together they can paint 7/24 of the room per hour, so it would take them 24/7 of an hour to paint a whole room and 24/7 * 5/6 to paint 5/6 of a room.

24/7 * 5/6 = 20/7 hours
Remember the one hour to add that Chris wasn't working, so it takes 20/7 + 1 = 27/7 hours total.
In hours and minutes that's 3 hours + 6/7 hr.
6/7 hr = 6*60/7 = 360/7 = 51 min 3/7 min
3/7 min = 60*3/7 sec = 180/7 sec = 25 5/7 sec
So 3 hrs, 51 min, 25.71 sec

Answer 2

Roger paints (1/6) of the room in each hour
Chris paints (1/8) of the room in each hour

Then together they paint (1/6) + (1/8) of the room in each hour

Lets assume that Chris took his break at the beginning. So, Roger has finished painting (1/6) of the room during that hour break. What is left is (5/6) of room unpainted.

Now, if they start working together, then:

[ (1/6) + (1/8) ] x = 5/6

where x = amount of time in hrs that it will take the rest of the room to be painted.

Solving for x gives:

x = 40/14 = 2.857 hrs

So, the total amont of time is = (2.857 + 1) hrs

= 3.857 hrs = 3 hrs and 51 minutes and 25 seconds

Answer 3

i think this is right,
i thought of it as a distance problem (d=rt) distance = rate X time

"distance"= 1 room
rate=chris-8hr/1room and roger- 6hr/1room
time=X
soo...
1=[1(6)+1(8)] t
1=14t
t=1/14
1/14 X 60=4.29
.29 X 60 =17.4
4 hours 17 minutes + 1 hour (chris's break)= 5 hours 17 mins...
I hope that it correct... sorry if its not