Lesson: Work Questions

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I solved a slightly different way: B+40/40B=1/24. Then 24(B+40)=40B. And solved for B to get 60 minutes.
gmat-admin's picture

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

Machines X and Y produced identical bottles at different constant rates. Machines X. operating alone of 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot?

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.
gmat-admin's picture

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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