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Car Assembly Plant...

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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.

Jun 26, 2018

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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

Jun 27, 2018