If Sam takes 6 hours to paint a house, and Pat takes 12 hours to paint the same house; how long with it take the 2 men to paint the same house together? What is the correct formulary?
In my head: Sam can do two houses in 12 hours, Pat can do one. Toghter, 3 houses in 12 hours, or 4 hours per house..
formulary:
total houses=rate*time
1 house=((1house/6hours) + (1 house/12hours) * time
1 = ((2+1)/12)time
time = 12/3 hours
Thank you
To find out how long it will take the two men to paint the house together, we can use the concept of work rates. The general formula to calculate work rate is:
Work Rate = Amount of Work / Time
In this case, the amount of work is painting the house, and the time is the number of hours it takes each person to complete the task individually. Let's assign variables to the work rates:
Sam's work rate = 1 house / 6 hours (since he paints 1 house in 6 hours)
Pat's work rate = 1 house / 12 hours (since he paints 1 house in 12 hours)
To find their combined work rate, we need to sum their individual work rates:
Combined work rate = Sam's work rate + Pat's work rate
Let's substitute the values and calculate their combined work rate:
Combined work rate = 1/6 + 1/12
= 2/12 + 1/12
= 3/12
= 1/4
So, their combined work rate is 1/4 of a house per hour.
To determine how long it will take the two men to paint the house together, we need to find the reciprocal of the combined work rate and convert it to hours:
Time = 1 / Combined work rate
= 1 / (1/4)
= 4 hours
Therefore, it will take the two men 4 hours to paint the house together.