For example: If it takes person A 1 hour to paint a house, person B 2 hours to paint the same house, and person C 3 hours to paint the same house, how long would it take if they all painted together?
2007-08-01 10:35:43 · 4 answers · asked by Guitarnoob 2 in Science & Mathematics ➔ Mathematics
1/1 + 1/2 + 1/3 = 1/x
x = time they would take to paint house together
2007-08-01 10:40:24 · answer #1 · answered by Tom B 2 · 0⤊ 0⤋
A paints 1 house in an hour.
B paints 1/2 house in an hour.
C paints 1/3 house in an hour.
Together they paint 1 + 1/2 + 1/3 = 11/6 houses in an hour, and therefore they paint 1 house in 6/11 hour.
2007-08-01 10:41:34 · answer #2 · answered by Anonymous · 0⤊ 0⤋
So the rate (houses per hour) of person A is 1 house / 1 hour.
The rate of person B is 1 house / 2 hours.
The rate of person C is 1 house / 3 hours.
Assuming they don't get in each other's ways as they are painting, you would add the rates together to get the speed of painting.
1 + 1/2 + 1/3 = 11/6. So you know that together they can paint 11 houses in 6 hours. Or, to paint one house it takes 6/11 hours.
So, for a general formula,
Time to paint one house = 1 / (sum of their rates)
2007-08-01 10:40:40 · answer #3 · answered by sharky.mark 4 · 0⤊ 0⤋
You need to convert them into hourly rates:
A paints 1 house/hour
B paints 1/2 house/hour
C paints 1/3 house/hour
The rate of A, B, and C all working together is just the sum of their rates:
(1 + 1/2 + 1/3) houses/hour =
(1 5/6) houses/hour
To paint 1 house at 11/6 houses/hour, it takes
1 / (11/6) = 6/11 hours, just over a half-hour.
2007-08-01 10:40:34 · answer #4 · answered by McFate 7 · 0⤊ 0⤋