Question 438028
Sally can clean the house in 6 hours her father can clean the house in 4 hours
 and her younger brother dennis can completely mess up the house in 8 hours
 if sally and her father clean and Dennis plays how long will it take to clean the house?
:
Let t = time required when all three are involved
:
Clean is positive
Messing = negative, obviously
:
Let a cleaned house = 1
:
{{{t/6}}} + {{{t/4}}} - {{{t/8}}} = 1
Multiply by 24
24*{{{t/6}}} + 24*{{{t/4}}} - 24*{{{t/8}}} = 24(1)
Cancel the denominators, results:
4t + 6t - 3t = 24
:
7t = 24
t = {{{24/7}}}
t = 3{{{3/7}}} hrs which is 3 + {{{3/7}}}*60 = 3 hrs 25.7 min