Three groups of people are in competition with each other at an automobile assembly plant:

Group A consists of 5 men and 6 women

Group B consists of 6 men and 8 women

Group C consists of 8 men and 3 women

Group A can assemble 16 cars in 8 hours

Group B can assemble 38 cars in 15 hours

How many cars can Group C assemble in 10 hours? Consider that all men work at the same level, and all women work at the same level, but the productivity level of the men is not the same as the productivity level of the women. Thank you for help.

Guest Jun 26, 2018

#1**+1 **

If group A can assemble 16 cars in 8 hours, they can build 2 cars per hour

So each hour in this group....we have 5 labor hours for the men and 6 labor hours for the women

And group B can assemble 38 cars in 15 hours, so they can build 38/15 cars per hour

And each hour in this group, we have 6 labor hours for the men and 8 labor hours for the women

And call the portion of a car built by a man in one hour 1/x

And call the portion of a car built by a women in one hour 1/y

So....we have this system

5 (1/x) + 6 (1/y) = 2

6(1/x) + 8(1/y) = 38/15

Solving this system produces x = 5 and y = 6

So....a man can produce 1/5 of a car per hour and a women produce 1/6 car per hour

So for group C which consists of 8 men and 3 women.....

The number of cars produced in 10 hours is :

8 man hrs per hour * (portion of a car produced by a man in one hour) * 10 hours plus

3 women hrs per hour * (portion of a car produced by a women in one hour) * 10 hours =

8 (1/5) (10) + 3(1/6)(10) =

80/5 + 30/6 =

16 + 5 =

21 cars

CPhill Jun 27, 2018