10. A house painter can finish a house in 6 hours. His partner can finish the same house in 12 hours. Which of the
following is the number of hours it would have taken them to finish painting the house if they had worked together?
A. 3 hours
B. 4 hours
C. 6 hours
D. 9 hours
1/x = 1/6 + 1/12
x = 4
To find the number of hours it would have taken them to finish painting the house if they had worked together, we can use the formula:
1/Time taken by painter + 1/Time taken by partner = 1/Time taken when working together.
Let's calculate the value using the given information:
Painter's time = 6 hours.
Partner's time = 12 hours.
1/6 + 1/12 = 1/Time taken when working together.
To simplify the equation, we need to find the common denominator, which is 12.
2/12 + 1/12 = 1/Time taken when working together.
3/12 = 1/Time taken when working together.
Now, we can find the time taken when working together:
Time taken when working together = 12/3.
Time taken when working together = 4 hours.
So, the correct answer is B. 4 hours.
To find the number of hours it would have taken them to finish painting the house if they had worked together, we can use the concept of work rates.
Let's consider the work rate of the house painter. We are given that the painter can finish the house in 6 hours, so his work rate is 1/6th of the house per hour. Similarly, his partner can finish the house in 12 hours, so his work rate is 1/12th of the house per hour.
When two people work together, their work rates are added up. So, the combined work rate of the house painter and his partner can be calculated as (1/6 + 1/12) = (2/12 + 1/12) = 3/12 = 1/4th of the house per hour.
To finish the entire house, the combined work rate should be equal to 1. Therefore, it would take them 4 hours to finish painting the house if they worked together.
So, the correct answer is B. 4 hours.