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

Question

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

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

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Bunuel · Accepted Answer

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

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

gmatophobia · Answer

Let's represent the information in tabular format as shown below - Screenshot 2023-05-14 130339.jpg Concept : If a person A can finish a work in T_1 hours working independently and person B can finish the same work in T_2 hours working independently, then working together A and B can finish the work in \frac{T_1 * T_2 }{ T_1 + T_2} hours Given Mary and Jim can assemble a model car in 12 hours and Mary takes 30 hours to assemble the car by herself. Assume that it takes Jim J_A hours to assemble the car by himself. Applying the concept discussed above: 12 = \frac{J_A * 30}{J_A + 30} 12*J_A + 360 = 30*J_A 12*J_A + 360 = 30*J_A 18J_A = 360 J_A = 20 Therefore it takes 20 hours for Jim to paint the car by himself. Mary and Jim can paint the model car in 4 hours and Jim takes 12 hours to paint the car by herself. Assume that it takes Mary M_P hours to assemble the car by herself. Applying the concept discussed above: 4 = \frac{M_P* 12}{M_P+12} 4*M_P + 48 = 12*M_P 8*M_P = 48 M_P = 6 Therefore it takes 6 hours for Mary to paint the car by herself. Time taken if Jim assembles the car and Mary immediately paints it after he is finished = 20 + 6 = 26 hours Option A

Aks111 · Answer

For work time questions, the easiest approach is to think in terms of number of units of work.

1. # of hrs to Assemble: 
Mary and Jim together = 12 hrs
Mary alone = 30 hrs
Let # number of units of work = 60 units (e.g., say 60 parts are to be assembled)
Rate of assembly for Mary and Jim together = 60/12 = 5 units / hr
Rate of assembly for Mary alone = 60/30 = 2 units / hr
=> Jim alone assembles at rate of 3 units / hr.
Therefore # of hrs it takes Jim alone to assemble = 60/3 = 20 hrs ............ (a)

2. # of hrs to paint: 
Mary and Jim together = 4 hrs
Jim alone = 12 hrs
Let # number of units of work = 24 units (e.g., say 24 Litre of paint is to be sprayed)

Rate at which Mary and Jim together paint = 24/4 = 6 units / hr
Rate of assembly of Jim alone = 24/12 = 2 units / hr
=> Mary alone assembles at rate of 4 units / hr.
Therefore # of hrs it takes Mary alone to paint = 24/4 = 6 hrs ............. (b)

# of hrs taken if Jim assembles the car and Mary immediately paints = 20 + 6 = 26 hrs

Answer: A

RICHA1189 · Answer

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

bumpbot · Answer

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

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