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?
number of workdays to do the house = 15(12) or 180
so 20 workers could do in 180/20 or 9 days
To solve this problem, we need to determine the number of days it would take for the increased number of painters to paint the houses.
Let's first calculate the rate at which the fifteen painters can paint the houses. We know that fifteen painters can paint the houses in 12 days:
Rate of fifteen painters = 1 house / 12 days
Now, let's consider the increased number of painters. If the number of painters is increased by 5, then we have a group of twenty painters.
Rate of twenty painters = 1 house / x days
To find the value of x, we can set up a proportion:
Rate of fifteen painters / Rate of twenty painters = 12 days / x days
Substituting the given rates:
(1 house / 12 days) / (1 house / x days) = 12 days / x days
We can simplify this equation:
1 / 12 = 12 / x
To solve for x, we can cross-multiply:
x = 12 * 12
x = 144
Therefore, the increased number of painters would take 144 days to paint the houses.
To determine how many days less it would take for the increased number of painters, we can subtract the original number of days from the new number of days:
12 days - 144 days = -132 days
The negative value indicates that it would take less time for the increased number of painters to paint the houses. However, in a real-world scenario, it's not possible to have negative time. Therefore, we can conclude that it would take 132 days less for the increased number of painters to paint the houses.