M07-03

Official Solution:

In a toy factory, when working together, Mary and Jim can assemble a model car in 12 hours and paint it in 4 hours. If it takes Mary 30 hours to assemble the car by herself, and it takes Jim 12 hours to paint the car by himself, then how many hours will it take if Jim assembles the car and Mary immediately paints it after he is finished?

A. 26
B. 24
C. 22
D. 20
E. 18


Let's divide the problem into two components: the assembly and the painting of the model car.

When it comes to assembling the car, Mary can complete the task alone in 30 hours, giving her an assembly rate of \(\frac{1}{30}\) job/hour.

When Mary and Jim work together, they can assemble the car in 12 hours. This gives \(\frac{1}{30} + \frac{1}{x}= \frac{1}{12}\), where \(x\) is the time it would take for Jim to assemble the car by himself. Solving this equation, we find that \(x=20\) hours.

Now, let's consider painting the car. Jim can complete this task alone in 12 hours, which means his painting rate is \(\frac{1}{12}\) job/hour.

When Mary and Jim work together, they can paint the car in 4 hours. This give the equation \(\frac{1}{y}+\frac{1}{12}=\frac{1}{4}\), where \(y\) is the time it would take for Mary to paint the car by herself. Solving this equation gives us \(y=6\) hours.

Finally, to find out the total time it would take if Jim assembles the car and Mary immediately paints it once he finishes, we simply add the time it takes each of them to complete their tasks individually. Therefore, \(x + y=26\) hours.


Answer: A