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## Comment on

Work Questions## I solved a slightly different

## You're referring to the

You're referring to the question at 6:20.

Good work!

## Machines X and Y produced

1. Machine X produced 30 bottles per minute.

2. Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.

My question concerns statement 2:

Machine “X” produced twice as many bottles in 4 hours as Machine “Y” produced in 3 hours.

4x = 2(3y)

4x = 6y

2x=3y

So, X=3/2y or Y=2/3x.

I understand that x = twice as many bottles as “Y” and that “Y” produces 2/3 as many bottles as “X” in the amount of time give (maybe I’m confused)

Here we go: using X=3/2y

If “Y” produced say 6 bottles then “x” should equal 18 bottles, right? But it equals 9.

9/9 +6 = 9/15 =3/5 not the 2/3

Brent, what is wrong with my thinking? I’m a bit frustrated here. I think I’m missing something somewhere with my reasoning. Please help. Thank you.

## Question link: https:/

Question link: https://gmatclub.com/forum/machines-x-and-v-produced-identical-bottles-a...

When assigning variables, it's important to make sure you understand what each variable represents.

At the beginning of your solution, you have 4x = 2(3y)

What do x and y represent?

x = the Machine X's RATE (per hour)

y = the Machine Y's RATE (per hour)

So, in 4 hours, Machine X's OUTPUT = 4x

In 3 hours, Machine Y's OUTPUT = 3y

So, 4x + 3y = the OUTPUT for the entire job

In your solution, you noted that 2x=3y

So, let's take the above equation and replace 3y with 2x to get:

4x + 2x = the OUTPUT for the entire job

So, 6x = the OUTPUT for the entire job

In other words, working at a RATE of x "things" per hour, Machine X can complete the entire job in 6 hours.

Cheers,

Brent

## Thanks Brent

I tend to over complicate and over think "Rate Problems'' more so than any other type of problem. They are definitely my weakest point and greatest frustration.

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