A worker can load 1 full truck in 6 hours. A second worker..

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AAPL: Moderator; Posts: 2710; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Tue Feb 20, 2018 6:25 am

A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill 1 truck?

A. 0.15
B. 0.31
C. 2.47
D. 3.23
E. 3.25

The OA is D.

First worker rate will be, 1/6 truck per hour.

Second worker rate will be, 1/7 truck per hour.

Then, their combined rates if they working together will be, 1/T = 1/6+1/7. Then T = (6*7)/(6+7) = 42/13 = 3.23 hours.

Is there a strategic approach to this PS question? Can any experts help, please? Thanks!

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Source: Beat The GMAT — Problem Solving | Tue Feb 20, 2018 6:25 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Tue Feb 20, 2018 7:43 am

AAPL wrote:A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill 1 truck?

A. 0.15
B. 0.31
C. 2.47
D. 3.23
E. 3.25

The OA is D.

First worker rate will be, 1/6 truck per hour.

Second worker rate will be, 1/7 truck per hour.

Then, their combined rates if they working together will be, 1/T = 1/6+1/7. Then T = (6*7)/(6+7) = 42/13 = 3.23 hours.

Is there a strategic approach to this PS question? Can any experts help, please? Thanks!

Well, if it were the case that we had two people, each of whom could perform a task individually in 6 hours, we know that if they worked together, they'd do the job in half the time, or in 3 hours. So because one of the individuals does the job in 7 hours, the answer has to be a little more than 3, leaving us with just D or E.

(My sense is that the GMAT would probably have been a little more artful about its answer choices, allowing you to use logic to determine which was correct without requiring much arithmetic.)

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Feb 20, 2018 4:15 pm

AAPL wrote:A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill 1 truck?

A. 0.15
B. 0.31
C. 2.47
D. 3.23
E. 3.25

One approach is to assign a nice value to the entire job (of filling a truck)

We want a number that works well with the given times (6 hours and 7 hours)
42 is such a number.
So, let's say that filling the truck is equivalent to shoveling 42 scoops of dirt into it.

A worker (we'll call worker A) can load 1 full truck in 6 hours
Rate = output/time = 42 scoops/6 hours = 7 scoops/hour
So, worker A's RATE is 7 scoops/hour

Worker B) can load 1 full truck in 7 hours
Rate = output/time = 42 scoops/7 hours = 6 scoops/hour
So, worker B's RATE is 6 scoops/hour

So, their COMBINED rate = 7 scoops/hour + 6 scoops/hour
= 13 scoops/hour

Worker B) Approximately how long, in hours, will it take them to fill 1 truck?
Time = output/rate
= 42 scoops/13 scoops/hour
= 42/13 hours
= 3 3/13 hours

ASIDE: Notice that 3 3/12 hours = 3.25 hours
So, 3 3/13 hours will equal a little less than 3.25 hours

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Tue Feb 20, 2018 6:57 pm

Hi AAPL,

We're told that A worker can load 1 full truck in 6 hours, a second worker can load the same truck in 7 hours and both workers load one truck simultaneously while maintaining their constant rates. We're asked for the approximate amount of time, in hours, that it will take them to fill 1 truck. This is an example of a standard 'Work Formula' question.

Work = (A)(B)/(A+B) where A and B are the individual times it takes the two entities to complete the task on their own.

Here, the two values would be 6 and 7...

(6)(7)/(6+7) = 42/13 = 3 3/13 hours

Since 3/13 is LESS then 3/12 = 1/4, the correct answer has to be a little less than 3 1/4 hours

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Thu Feb 22, 2018 8:34 am

AAPL wrote:A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill 1 truck?

A. 0.15
B. 0.31
C. 2.47
D. 3.23
E. 3.25

The combined rate of the two workers is 1/7 + 1/6 = 6/42 + 7/42 = 13/42.

Since time is inverse of rate, it will take 42/13 = 3 3/13 = 3.23 hours.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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