A company contracts to paint 3 houses. Mr.Brown can paint a house in 6 days while Mr.Black would take 8 days and Mr.Blue 12 days. After 8 days Mr.Brown goes on vacation and Mr. Black begins to work for a period of 6 days. How many days will it take Mr.Blu to paint?
Mr. Brown painted the first whole house in 6 days plus 1/3 of the second house in the next 2 days. Mr. Black can paint a whole house in 8 days and had 8 days to work, so he painted the equivalent of 1 whole house. That accounts for 2-1/3 houses painted. Mr. Blue only needs to paint 2/3 of the last house, so 2/3 times 12 days equals 8 days.
(V) brown=1house/6days=3house/18days
(V) black= 1house/8days=3house/24days
(V) blue= 1house/12days=3house/36days
(3house*8days/18days)+(3house*8days/36days)=1.5house
(3house*6days/24days)+(3house*Xdays/36days)=1.5house===>X=9days takes Mr blue
Mr. Brown painted the first whole house in 6 days plus 1/3 of the second house in the next 2 days. Mr. Black can paint a whole house in 8 days and had 8 days to work, so he painted the equivalent of 1 whole house. That accounts for 2-1/3 houses painted. Mr. Blue only needs to paint 2/3 of the last house, so 2/3 times 12 days equals 8 days.