One person can paint a room in 5 hours and the other takes 8 hours working together how long will it take the two of them if they're working together work the problem out and explain it to me

Ok so find how much work each can do per hour

irst person is 5 hours to do all room
therefor
1 hour=1/5 room

2nd person takes 8 hours to do all room
therefor
1 hour=1/8 room

since working together, add times

1 hour=1/5+1/8
make denoms same
1hour=8/40+5/40=13/40

13/40 room times x hours=1 whole room
multiply both sides by 40/13 to cleaf raction (13/40 times 40/13=520/520=1)

xhours=40/13hours
xhours=3 and 1/13 hours