Algebra 1/2 Word Problem

Question

Phil can paint a room in 4 hours. He paints the room for 2 hours, then takes a break to have lunch. During which, his younger brother Nick takes over and paints the room for 1 hour (he can paint a room by himself in 5 hours). After, Phil comes back to help his brother finish the job. How much longer did they spend painting the room?

Answer 1

40 minutes

assuming their working together doesn't interfere with each other or complement each other

together they can paint the room in x hours

1/4 + 1/5 = 1/x, multiply by 20 and solve for x

5+4=20/x

9=20/x

9x =20

x = 20/9 = 2.222...

together they can paint the room in 2 hours and 2/9 of an hour or 2 hours + 13 minutes + 20 seconds

Phil painted half the room in 2 hours

Nick painted 1/5 of the room in 1 hour

that adds to 1/2+1/5 = 5/10 + 2/10 = 7/10 of the room, leaving 3/10 of the room

20/9 times 3/10 = 2/3 of an hour or 40 minutes