A painter can paint a building in 4 days and his apprentice 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 works alone?
Answers
Answer:
The area of the building painted by the painter in one day = 1/4
The area of a building painted by the apprentice = 1/6
Assuming that the painter is I'll on the first day,
The apprentice paints 1/6 of the building.
When they work together, they paint
1/6 + 1/4 = 5/12 of the building.
Let the number of days they work together be 'x'.
1/6 + (5/12) x = 1 [ As 1 represents the total area of the building]
(5/12)x = 1 - 1/6 = 5/6
x = (5/6)(12/5) = 2
So they together for two days.
Total number of days taken = 2 + 1 = 3
[ Because the apprentice worked alone for one day]
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 [We will add 1 as there was only 1 painter painted the building 1 day ]
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