Answer:
To determine how long it will take for Henry, Ruby, and Charlie to paint one small house together, you can use the concept of "work rates." The work rate is the fraction of a house that each person can paint in one day. Then, you can add their work rates to find the combined rate for all three.
- Henry can paint a house in 3 days, so his work rate is 1/3 of a house per day.
- Ruby can paint a house in 4 days, so her work rate is 1/4 of a house per day.
- Charlie can paint a house in 5 days, so his work rate is 1/5 of a house per day.
Now, add their work rates together:
1/3 (Henry's rate) + 1/4 (Ruby's rate) + 1/5 (Charlie's rate)
To add these fractions, you need a common denominator. In this case, the least common multiple of 3, 4, and 5 is 60. So, you can rewrite the fractions with a common denominator:
(20/60) + (15/60) + (12/60)
Now, add the fractions:
(20 + 15 + 12) / 60 = 47/60
So, Henry, Ruby, and Charlie together can paint 47/60 of a small house in one day. To find out how long it takes them to paint one small house, take the reciprocal of this fraction (flip it):
1 / (47/60) = 60/47
It will take them 60/47 days to paint one small house together, which can be simplified as a mixed number:
1 day and 13/47 days
So, it will take them approximately 1 day 13 hours, and 11 minutes to paint one small house together.