If Robert can assemble a model car in 30 minutes...

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BTGmoderatorLU: Moderator; Posts: 2558; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Thu Feb 15, 2018 5:25 am

If Robert can assemble a model car in 30 minutes and Craig can assemble the same model car in 20 minutes, how long would it take tehm, working together, to assemble the model car?

A. 12 minutes
B. 13 minutes
C. 14 minutes
D. 15 minutes
E. 16 minutes

The OA is A.

I'm confused by this PS question. Experts, any suggestion? Thanks in advance.

How can I determine the rate of each one? Can I say that the model car has a n number of pieces?

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Source: Beat The GMAT — Problem Solving | Thu Feb 15, 2018 5:25 am

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

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by ErikaPrepScholar » Thu Feb 15, 2018 7:32 am

The easiest approach on this question is to use the combined work equation $$\frac{1}{A}+\frac{1}{B}=\frac{1}{A and B}$$ Where A and B are the time it would take each person (or machine, pump, printer, etc. depending on the question) to finish a job alone, and A and B is the time it would take both to finish the same job together.

In this problem, A will be the time it takes Robert to assemble the model car alone, B will be the time it takes Craig to assemble the model car alone, and A and B will be the time it takes the two of them to assemble the model car together. Plugging in the information from our equation gives: $$\frac{1}{20}+\frac{1}{30}=\frac{1}{A\ and\ B}$$ Then solving for A and B gives $$\frac{3}{60}+\frac{2}{60}=\frac{1}{A\ and\ B}$$ $$\frac{5}{60}=\frac{1}{A\ and\ B}$$ $$5\left(A\ and\ B\right)=60$$ $$A\ and\ B=12$$ So Robert and Craig can assemble the model car together in 12 minutes, and the correct answer is A.

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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 » Thu Feb 15, 2018 12:32 pm

LUANDATO wrote:If Robert can assemble a model car in 30 minutes and Craig can assemble the same model car in 20 minutes, how long would it take tehm, working together, to assemble the model car?

A. 12 minutes
B. 13 minutes
C. 14 minutes
D. 15 minutes
E. 16 minutes

The OA is A.

I'm confused by this PS question. Experts, any suggestion? Thanks in advance.

How can I determine the rate of each one? Can I say that the model car has a n number of pieces?

If 'A' is the amount of time for one entity to complete a job, and 'B' is the amount of time for a second entity to complete the same job, then the time for the two to complete the job together is (A*B)/(A + B)

A= 30 minutes
B= 20 minutes

A*B/(A+B) = 30*20/(30+20) = 30*20/50 = 30*2/5 = 60/5 = 12. The answer is A

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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 » Thu Feb 15, 2018 12:33 pm

LUANDATO wrote:If Robert can assemble a model car in 30 minutes and Craig can assemble the same model car in 20 minutes, how long would it take tehm, working together, to assemble the model car?

A. 12 minutes
B. 13 minutes
C. 14 minutes
D. 15 minutes
E. 16 minutes

The OA is A.

I'm confused by this PS question. Experts, any suggestion? Thanks in advance.

How can I determine the rate of each one? Can I say that the model car has a n number of pieces?

Note that the formula (A*B)/(A + B) = T is really the same one that Erika used. If the first rate is 1/A and the second rate is 1/B the combined rate is 1/A + 1/B, which comes out to (A+B)/A*B. Because rate and time have a reciprocal relationship, a rate of (A+B)/A*B is equivalent to a time of A*B/(A + B)

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Jun 23, 2019 10:30 am

BTGmoderatorLU wrote:If Robert can assemble a model car in 30 minutes and Craig can assemble the same model car in 20 minutes, how long would it take tehm, working together, to assemble the model car?

A. 12 minutes
B. 13 minutes
C. 14 minutes
D. 15 minutes
E. 16 minutes

The combined rate of Robert and Craig is 1/20 + 1/30 = 3/60 + 2/60 = 5/60. We can interpret this rate as "They can assemble 5 model cars in 60 minutes." Since time is the reciprocal of rate, it would take them 60/5 = 12 minutes to complete one car.

Answer: A

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