assembly line

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mehrasa Master | Next Rank: 500 Posts
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assembly line

Post Thu Mar 26, 2015 7:44 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    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

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    talaangoshtari Master | Next Rank: 500 Posts
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    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.

    Thanked by: mehrasa
    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

    _________________
    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

    Thanked by: mehrasa
    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    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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