Fifteen painters can paint a number of houses in 12 days .if the number of painters is increased by 5, how many days less would it take the painters working at the same rate to paint the houses?
clearly a painter can paint 1/180 of the job in one day. So, 20 painters can paint
20/180 = 1/9 of the job in a day, making the total 9 days.
So, it takes 3 days less.
Not also that you could reason that if the number of painters is increased by a factor of 5/4, the time taken is reduced by that factor.
4/5 of 12 = 9
To solve this problem, let's break it down step by step.
Step 1: Calculate the number of painters required to paint one house in one day.
Since 15 painters can paint a number of houses in 12 days, we need to find out how many painters are required to paint one house in one day. We calculate this by dividing the number of painters (15) by the number of days (12):
15 painters / 12 days = 1.25 painters per day for one house.
Step 2: Calculate the number of days required for 20 painters to paint the given number of houses.
Since the number of painters is increased by 5, the total number of painters becomes 20. We need to find out how many days it will take for 20 painters to paint the houses at the same rate. We calculate this by using the painters per day value obtained in step 1:
1.25 painters per day × 20 painters = 25 painters per day for 1 house.
Step 3: Calculate the number of days required for 20 painters to paint the houses.
To find the number of days required, we divide the total number of houses by the number of houses painted in one day:
Number of days = Total number of houses / Houses painted in one day
Let's assume the number of houses is x.
For 15 painters, it takes 12 days to paint x houses, so the number of houses painted in one day by 15 painters is:
x houses / 12 days = 1 house per 12 days.
For 20 painters, it will take y days to paint the same number of houses, so the number of houses painted in one day by 20 painters is:
x houses / y days = 1 house per y days.
Since the same number of houses is being painted, we can equate the two expressions:
1 house per 12 days = 1 house per y days.
Now, we can solve for y:
12 days = y days
y = 12 days.
Therefore, it would take the painters 12 days to paint the houses when the number of painters is increased by 5.
To find out how many days less it would take, we can compare the original number of days (12 days) to the new number of days (12 days). In this case, there is no difference in the number of days.
So, the answer is 0 days less.