Question 755002: 3 painters took 15 hours to paint a house. How long would it take for 9painters to do the same Found 2 solutions by josgarithmetic, DrBeeee:Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website! From this part, "3 painters took 15 hours to paint a house.", determine how long it took 1 painter to paint the house, assuming each painter uses the same rate. One painter needs three times longer than all three working together. What is 3 times 15?
45 hours for 1 painter to paint the house.
Now you want the time for 9 painters? Their rates are simply added.
You can put this solution on YOUR website! Solving this problem can be done by calculating "man-hours" to do the job, namely, paint a house.
Let MH = number of man-hours to paint a house. From the problem statment,"takes 3 painters (or "men"), 15 hours to paint a house, we get
(1) MH = 3*15 or
(2) MH = 45 painter-hours.
Now we want to know how long it will take 9 painters to do the same painting job. The answer is given by
(3) Number of hours = (Number of painter-hours required)/(number of painters) or
(4) Number of hours = MH/9 or
(5) Number of hours = 45/9 or
(6) Number of hours = 5
Answer: It will take 9 painters five hours to paint a house that takes 15 hours for 3 painters to paint.
Comment: The reason that this problem can be solved by simply using manhours is that we have the equivalent of 3 equal groups of 3 painters each. Beware other such problems require more analysis. Look in the archieve of problems of this type to learn more.
(
