SOLUTION: A painter can paint a building in 4 days and his appretice can do it in 6 days. How long will it take them to paint this building if they work together on it except for 1 day when

Question 327363: A painter can paint a building in 4 days and his appretice can do it in 6 days.
How long will it take them to paint this building if they work together on it except for 1 day when the painter is ill and the apprentice work alone.?
Found 2 solutions by ganeshindia, AAfter Search:
Answer by ganeshindia(11) (Show Source): You can put this solution on YOUR website!
Let the amount of total work be 1.
The work done by the painter in one day = 1/4 of the total work.
The work done by the apprentice in one day = 1/6 of the total work.
The work done by the two people together in one day = 1/4 + 1/6 = 5/12 of the total work.
1/6 of the total work is done by the apprentice alone for one day.
The remaining 5/6 of the total work is done by the painter and apprentice together for x days.
Therefore x = amount of work / work done in one day = (5/6)/(5/12) = 2 days.
Therefore, number of days taken to complete the work = 2 + 1 = 3 days.
Answer by AAfter Search(61) (Show Source): You can put this solution on YOUR website!
In 4 days the painter completes the whole work W.
In 1 day the painter completes 1/4 work.
In 1 day the apprentice completes 1/6 work.
Let the number of days taken to complete the work by them be n days.
Hence nW/6 + (n - 1)W/4 = W
=> n/6 + (n - 1)/4 = 1
=> 2n + 3n - 3 = 12
=> 5n = 15
=> n = 3
Hence the work is completed in 3 days.
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