Solve the problem and answer the question.
-A painter can finish painting a house in 7 hours. Her assistant takes 9 hours to finish the same job. How long would it take for them to complete the job if they were working together?
B) 8 hr
D) 6 hr

Question

Solve the problem and answer the question.
-A painter can finish painting a house in 7 hours. Her assistant takes 9 hours to finish the same job. How long would it take for them to complete the job if they were working together?
B) 8 hr 
D) 6 hr

Quizplus · Accepted Answer

Let's use the formula:
Time = Work / Rate
Let the amount of work be represented by 1 (the whole job). 
The rate of the painter is 1/7 (finishing 1 job in 7 hours). 
The rate of the assistant is 1/9 (finishing 1 job in 9 hours). 
When working together, their rates will add up so:
1 = (1/7 + 1/9) * Time
1 = (16/63) * Time
Time = 6.3 hours or approximately 6 hours and 18 minutes. 
The closest answer choice to that is C (6 hours). Let x be the time it takes for them to complete the job when working together.
Then, the amount of work done by the painter in one hour is 1/7 and the amount of work done by the assistant in one hour is 1/9.
Working together, they can finish the job in one hour, which means the amount of work done in one hour is 1/x.
So, we can set up the equation:
1/7 + 1/9 = 1/x
Solving for x, we get x = 63/16, which is approximately equal to 3.94 hours or 3 hours and 56 minutes.
Therefore, the best choice is C, which is closest to the calculated value of 3.94 hours.

Solve the Problem and Answer the Question