To paint a house, two painters are hired. the first painter can paint the house in ten hours. the second painter will need six hours to paint the entire house. if the two painters start painting at 8: 00 am, at what time will they finish painting the house?

So
p1 can paint hours in 10 hours, so 1/10 house per 1 hour

p2 can paint house in 6 hours so 1/6 house per 1 hour

if both start at 8:00, when finish??
find how many hours they take

1 hour=p1+p2=1/10+1/6
just add 1/10 and 1/6 and see how many to get 1/1 house done
1/10+1/6=3/30+5/30=8/30=4/15
xhours times 4/15=1
multiply both sides by 15/4 to clear fraction
xhours =15/4
xhours=3 and 3/4

they take 3 and 3/4 hours aka 3 hours and 45 mins so
8:00+3:45=11:45

they finish at 11:45 AM