Question

Bill can paint a small house in 3 days, Sharon can paint a small house in 4 days and Wilber can paint a small house in 5 days. How long will it take for Bill, Sharon and Wilber together to paint one small house? Give your answer a fraction.

Answer 1

To solve this problem, let us say that the action of totally painting a small house is called “1 job”. Therefore the rates of each person in painting the small house are:

Bill = 1 job / 3 days = 1 / 3

Sharon = 1 job / 4 days = 1 / 4

Wilber = 1 job / 5 days = 1 / 5

 

Therefore the total rate is calculated by simply adding the rates of the three.

(1 /  3) + (1 / 4) + (1 / 5) = 1 / x

where x is the number of hours it take if all them paint together

 

Calculating for by multiplying both sides by 60:

60 [(1 /  3) + (1 / 4) + (1 / 5) = 1 / x]

(60/3) + (60/4) + (60/5) = 60 / x

20 + 15 + 12 = 60 / x

47 = 60 / x

x = 60 / 47 hours

 

 

Answer:

60/47 hours