Eight workers from Company A can paint 7 homes in 84 hours. Working to

Hi All,

These types of layered "work" questions can sometimes be confusing to look at, but they're based on arithmetic, so you just have to be careful with your math and take good notes. Here's how to solve this problem step-by-step:

Let's break the prompt into pieces....

1) We're told that 8 workers from Company A can paint 7 homes in 84 hours. This means...

8 workers can paint 7 homes in 84 hours =
8 workers can paint 1 home in 12 hours

So, for those 12 hours, ALL 8 workers need to paint to get the job done. This means...
1 worker from Company A would need 8(12) = 96 hours to paint 1 home by himself.

2) We're told that 3 workers from Company A and 5 from Company B can paint 9 homes in 96 hours.

We already know that 1 worker from Company A can paint an ENTIRE HOME BY HIMSELF in 96 hours.
Those 3 workers from Company A will end up painting 3 (of the 9) homes in 96 hours.

This leaves 5 workers from Company B to paint 6 homes in 96 hours. This means...

5 workers can paint 6 homes in 96 hours =
5 workers can paint 1 home in 16 hours

So, for those 16 hours, ALL 5 workers need to paint to get the job done. This means....
1 worker from Company B would need (5)(16) = 80 hours to paint 1 home by himself

3) Now that we know the rate for each worker from Company B, we can answer the final question:

How many workers from Company B are required to paint 9 homes in 60 hours.

This final calculation can be done as a ratio or as a rate:

1 worker paints 1 home in 80 hours
4/3 workers paint 1 home in 60 hours
9 homes in 60 hours = 9(4/3 workers) = 36/3 = 12 workers

Final Answer:

GMAT assassins aren't born, they're made,
Rich