Adam and Brianna plan to install a new tile floor in a classroom. Adam

Question

Adam and Brianna plan to install a new tile floor in a classroom. Adam works at a constant rate of 50 tiles per hour, and Brianna works at a constant rate of 55 tiles per hour. If the new floor consists of exactly 1400 tiles, how long will it take Adam and Brianna working together to complete the classroom floor?

A. 26 hrs. 44 mins.
B. 26 hrs. 40 mins.
C. 13 hrs. 20 mins.
D. 13 hrs. 18 mins.
E. 12 hrs. 45 mins.

A. 26 hrs. 44 mins. 
B. 26 hrs. 40 mins. 
C. 13 hrs. 20 mins.
D. 13 hrs. 18 mins. 
E. 12 hrs. 45 mins.

PareshGmat · Accepted Answer

Rate of Adam = 50 tiles/hr

Rate of Brianna = 55 tiles/hr

Combined rate = 105 tiles/hr

Time required for 1400 tiles  = \frac{1400}{105} = \frac{40}{3} = \frac{39}{3} + \frac{1}{3} *60 = 13 Hours 20 Minutes

Answer = C

manpreetsingh86 · Answer

actually we don't need to all these complex calculations

w=1400 units
when adam and briana work together, they will lay 55+50=105 tiles in an hour.

therefore total time taken to lay 1400 tiles on the floor = 1400/105 = 40/3 hour
=13(1/3) hour or 13 hour and (1/3)*60 minutes
=13 hour and 20 minutes.

Gnpth · Answer

We need to find the individual time for Adam and Brianna to put the 1400 tiles.

Adam:  1400*\frac{1}{50} = 28 Hours.

Brianna :  1400*\frac{1}{55} =Mathematically it comes to 25.45. When we convert the decimal to time we get. 25 hours 27 Minutes.

Now the combined rate,

\frac{1}{A}  +  \frac{1}{B} =  \frac{1}{28}  +  \frac{1}{25.45}

=  \frac{(25.45 + 28)}{(712.6)}

=  \frac{53.45}{712.6}

Inverting this to get in hours.

=  \frac{712.6}{53.45}

=13. 33 Converting it into hours ==> 13 hours 19.8 Minutes => 13 hours 20 Minutes. Answer is C.

Bunuel : I hope you have some different approach to this problem. Please post your explanation.

HuongShashi · Answer

I usually go with " 1/A+1/B"... but this time I use strategy as you do. Are there any difference between 2 ways? THANKS

PareshGmat · Answer

Rate = 1/Time Rates have to be combined to calculate the time required working together. In this problem, rate per hour is given directly. So the reciprocal addition does not come in picture

rhine29388 · Answer

Adam installs at a constant rate of 50 tiles per hour
Brianna installs at a constant rate of 55 tiles per hour
If both persons work together they can install 105 tiles in a hour
Total number of installs to be done = 1400
time required for installation of 1400 tiles =  \frac{1400}{105}  = 13.3333 hrs = 13 hrs 20 mins
Correct answer - C

Mkrishnabdrr · Answer

W=R X T
or, R=W/T

Adam's Rate, A=50 tiles per hour
Brianna's Rate, B=55 tiles per hour

Combine rate (A+B) =50+55 =105 tiles per hour (We can ONLY ADD RATE of work in Work Rate problems)

105 tiles per hour
1 tile = 1/105 hour
1400 Tiles =1400/105 hour
 = 200/15 hours
 =40/3 hours
 =(39+1)/3
 =39/3 + 1/3 hours
 =13 hours + 1/3 x 60 min
 =13 hours and 20 minutes
Hence, Answer is:  C

Abhishek009 · Answer

\frac{1400}{(55+50)} = 13 \frac{1}{3}   Hrs

Thus, the correct answer must be (C)

ScottTargetTestPrep · Answer

Since Adam works at a constant rate of 50 tiles per hour and Brianna works at a constant rate of 55 tiles per hour, their combined rate is 105 tiles per hour.
 
If we let t = the time they work together, we have:
 
105t = 1400
 
t = 1400/105 = 280/21 = 13 7/21 = 13 ⅓ hours = 13 hours 20 mins.
 
Answer: C

TheMechanic · Answer

I am privileged to be among Super computers who solve this question within 1mins 20seconds. Guess I am too dumb to take close to 1min 45seconds to get through this!

sasyaharry · Answer

There is no need to find individual rates! We are already given that Adam and Brianna can lay tiles at the rate of 50 and 55 per hour.

In 1 hour they will 105 tiles.

105 tiles ------- 1 hour
1400 tiles-------  \frac{1400}{105}

\frac{14*100}{21*5}  =  \frac{14 * 20}{21}  =  \frac{7*2 * 20}{21}  =  \frac{40}{3}

= 13.333

.333 =  \frac{1}{3}  and \frac{1}{3}  of an hour is 20 minutes.

Hence the answer is 13 hours and 20 minutes.

EMPOWERgmatRichC · Answer

Hi All,

Although this question is presented in a "style" that is similar to a Work Formula question, it's actually just a Rate question.The rates can be combined into one big rate….

50 tiles per hour + 55 tiles per hour = 105 tiles per hour

You can now use the "Distance Formula" to answer this question….

D = R x T 
1400 tiles = (105 tiles/hour)(Time)

1400/105 = Time

13 1/3 hours = T

Final Answer:  C

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

RastogiSarthak99 · Answer

Hey Brianna's rate is 55tiles/hr and not 60tiles/hr. Small typo, but figured I would point it out anyway.

mm229966 · Answer

Together Adam and Brianna install 55+50=105 tiles in 1 H.

They'll need 1400/105 = 40/3 = 13 1/3 = 13.20 H. to finish installing the class floor C.

Abhishek009 · Answer

= \frac{1400}{(50+55)}

= \frac{1400}{105}

= 13 & 1/3Hours

= 13 Hours 20 Mins, Answer must be (C)

hemantbafna · Answer

50 + 55 = 105 tiles per hour

The question asks how long it will take them to set 1400 tiles.

Time = Work / Rate = 1400 tiles / (105 tiles / hour) = 40/3 hours = 13 and 1/3 hours = 13 hours and 20 minutes

C .

sanjeevsinha082 · Answer

Because Adam and Brianna are working together, add their individual rates to find 
their combined rate:
50 + 55 = 105 tiles per hour
The question asks how long it will take them to set 1400 tiles.
Time = Work / Rate = 1400 tiles / (105 tiles / hour) = 40/3 hours = 13 and 1/3 hours = 
13 hours and 20 minutes
The correct answer is C.

parthadlakha · Answer

Actually I took 40/3 = 13.3 Hours (13H 18m) But the official answer has take 40/3 = 13.33 (13H 20m). Is it a rule that we need to take our Quotient upto 2 decimal places?

EMPOWERgmatRichC · Answer

Hi parthadlakha, Depending on the information in the prompt (as well as how the answers are written), you would likely find it best to go to 2-3 decimal points in many cases - although if the answers were more 'spread out' in this prompt, then going to just 1 decimal point would have been fine. In the broader sense though, we're really talking about the overall accuracy of the calculation. When comparing 0.3 and 1/3, we're really talking about two notably different values (just ask anyone in banking, finance, etc.). In this prompt, 30% of an hour is (.3)(60 minutes) = 18 minutes, but 1/3 of an hour is (1/3)(60 minutes) = 20 minutes. Those extra 2 minutes are meaningful and have to be accounted for. Business Schools also expect that you will understand the difference. GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com

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