In a toy factory, when working together, Mary and Jim can assemble

Assemble toys
Mary and Jim can assemble car together in 12 hrs
Let the time taken by Mary to assemble be M and Jim be J
GIVEN M = 30 hrs

1/M + 1/J = 1/12
1/30+1/J = 1/12
1/J = 1/12- 1/30 = 1/20

Jim takes 20 hrs to assemble alone at constant rate

Paint car

Mary and Jim can paint car together in 4 hrs
Let the time taken by Mary to paint car be M and Jim be J
GIVEN J = 12 hrs

1/M +1/J = 1/12
1/12+1/M = 1/4
1/M = 1/4-1/12
M = 6 hrs

Mary will take 6 hrs to paint a car alone

Total time taken when JIM assembles the car and Mary paints the car = 20+6 = 26 hrs

Answer A

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