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assembly line

This topic has 3 expert replies and 1 member reply
mehrasa Master | Next Rank: 500 Posts
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assembly line

Post Thu Mar 26, 2015 7:44 am
assembly line alpha starts and creates widgets at a rate of 25 w per hour. exactly one hour later, assembly line beta begins production at a rate of 30 w per hour. in how many minutes will the two assembly line have produced the same number of widgets?

1) 5
2) 25
3) 250
4) 300
5) 350

I like to know the formula for this and how to solve it (i reached different number)

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GMAT/MBA Expert

Post Thu Mar 26, 2015 12:11 pm
mehrasa wrote:
assembly line alpha starts and creates widgets at a rate of 25 w per hour. exactly one hour later, assembly line beta begins production at a rate of 30 w per hour. in how many minutes will the two assembly line have produced the same number of widgets?

1) 5
2) 25
3) 250
4) 300
5) 350
An alternate approach is to PLUG IN THE ANSWERS. which represent the total time for Beta.
Since Alpha begins to work one hour earlier than Beta, Alpha's total time is 1 hour longer than Beta's total time.
When the correct answer choice is plugged in, Beta and Alpha will produce the same number of widgets.

Answer choices A and B seem way too small.
Of the remaining answer choices, start with the option in the middle (D).

Answer choice D: 300 minutes = 5 hours
At a rate of 30 widgets per hour, the number of widgets produced by Beta in 5 hours = r*t = 30*5 = 150.
At a rate of 25 widgets per hour, the number of widgets produced by Alpha in 6 hours = r*t = 25*6 = 150.
Success!

The correct answer is D.

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GMAT/MBA Expert

Post Thu Mar 26, 2015 10:32 am
Quote:
assembly line alpha starts and creates widgets at a rate of 25 w per hour. exactly one hour later, assembly line beta begins production at a rate of 30 w per hour. in how many minutes will the two assembly line have produced the same number of widgets?

A) 5
B) 25
C) 250
D) 300
E) 350
We can also solve this algebraically.

Let t = number of HOURS that assembly line beta works
So, t + 1 = number of HOURS that assembly line alpha works

Also, assembly line beta's rate = 30 widget per hour
And, assembly line alpha's rate = 25 widget per hour

Now, start with a WORD EQUATION...
# of widgets that assembly line alpha produces = # of widgets that assembly line beta produces
Production = (rate)(time)
So, (25)(t + 1) = (30)(t)
Expand: 25t + 25 = 30t
Rearrange: 25 = 5t
Solve: t = 5
So, assembly line beta must work for 5 HOURS

5 hours = 300 minutes.
Answer: D

Cheers,
Brent

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GMAT/MBA Expert

Post Thu Mar 26, 2015 8:09 am
mehrasa wrote:
assembly line alpha starts and creates widgets at a rate of 25 w per hour. exactly one hour later, assembly line beta begins production at a rate of 30 w per hour. in how many minutes will the two assembly line have produced the same number of widgets?

A) 5
B) 25
C) 250
D) 300
E) 350

I like to know the formula for this and how to solve it (i reached different number)
Assembly line alpha starts and creates widgets at a rate of 25 w per hour. Exactly one hour later, assembly line beta begins....
So, in that 1 hour, assembly line alpha makes 25 widgets.
In other words, assembly line alpha has a 25-widget lead on assembly line beta.

Exactly one hour later, assembly line beta begins production at a rate of 30 w per hour
So, EVERY HOUR, assembly line beta makes 5 widgets more than assembly line alpha.
Since assembly line alpha has a 25-widget lead on assembly line beta, it will take 5 HOURS for assembly line beta to make up for that 25-widget deficit.

in how many MINUTES will the two assembly line have produced the same number of widgets?
5 HOURS = 300 minutes
Answer D

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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talaangoshtari Master | Next Rank: 500 Posts
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21 May 2014
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1 members
Upvotes:
8
Post Thu Mar 26, 2015 8:25 am
h w_alpha w_beta

1 25 0
2 50 30
3 75 60
4 100 90
5 125 120
6 150 150

So, from the moment that they work together, it takes 5 hour or 300 minutes for producing the same number of widgets.

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