One machine, working at a constant rate, can fill a certain

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swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Tue Aug 21, 2018 10:17 am

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One machine, working at a constant rate, can fill a production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours

The OA is A.

Source: Veritas Prep

Source: Beat The GMAT — Problem Solving | Tue Aug 21, 2018 10:17 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Tue Aug 21, 2018 10:33 am

<p>

swerve wrote:</p>
One machine, working at a constant rate, can fill a production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours

It suffices to apply the generalization of the "taps shortcut", valid for any (finite) number of "taps".

The solution above follows the notations and rationale taught in the <b>GMATH</b> method.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

One machine, working at a constant rate, can fill a certain

by Brent@GMATPrepNow » Tue Aug 21, 2018 10:53 am

swerve wrote:One machine, working at a constant rate, can fill a production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours

The OA is A.

Source: Veritas Prep

Let's assign a "nice" value to the entire job (a value that works well with the given information)

Let's say the machine is making widgets and an order = 8 widgets.

One machine, working at a constant rate, can fill a production order in 8 hours.
In other words, ONE machine can make 8 widgets in 8 hours
This means, ONE machine makes 1 widget per hour

How long would it take four machines to fill the order?
If ONE machine makes 1 widget in ONE hour,
then FOUR machines makes 4 widgets in ONE hour,
which means FOUR machines makes 8 widgets in TWO hours

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Aug 21, 2018 11:06 am

Time and rate have a RECIPROCAL RELATIONSHIP.
If Mary works TWICE as fast as John, Mary's time will be 1/2 John's time.
If Mary works THREE TIMES as fast as John, Mary's time will be 1/3 John's time

swerve wrote:One machine, working at a constant rate, can fill a production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hour

Since 4 machines will work 4 times as fast as 1 machine, the time for 4 machines will be 1/4 the time for 1 machine:
(1/4)(8) = 2 hours.

The correct answer is A.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Aug 23, 2018 4:11 pm

swerve wrote:One machine, working at a constant rate, can fill a production order in 8 hours. How long would it take four identical machines, working at the same constant rate, to fill the order?

A. 2 hours
B. 4 hours
C. 8 hours
D. 16 hours
E. 32 hours

Since the rate of 1 machine is 1/8, the rate of 4 machines is 4/8 = 1/2.

Thus, it will take 4 machines 1/(1/2) = 2 hours to fill the order.

Answer: A

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