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

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Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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Tough and Tricky questions: Work/Rate.



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.
[Reveal] Spoiler: OA

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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Work/Rate.



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.



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.
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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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Gnpth wrote:
Bunuel wrote:

Tough and Tricky questions: Work/Rate.



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.



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.


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.
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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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Rate of Adam = 50 tiles/hr

Rate of Brianna = 60tiles/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
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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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New post 04 Jan 2015, 01:43
PareshGmat wrote:
Rate of Adam = 50 tiles/hr

Rate of Brianna = 60tiles/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



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
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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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HuongShashi wrote:
PareshGmat wrote:
Rate of Adam = 50 tiles/hr

Rate of Brianna = 60tiles/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



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



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 :)
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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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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
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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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New post 27 May 2017, 05:48
Bunuel wrote:

Tough and Tricky questions: Work/Rate.



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.


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:
[Reveal] Spoiler:
C

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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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New post 27 May 2017, 09:04
Bunuel wrote:

Tough and Tricky questions: Work/Rate.



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.

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

Thus, the correct answer must be (C)
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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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Quote:

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.


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
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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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New post 18 Sep 2017, 12:23
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! :sad: :cry:
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Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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New post 09 Nov 2017, 13:58
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.
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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam [#permalink]

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New post 08 Mar 2018, 11:43
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:
[Reveal] Spoiler:
C


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Re: Adam and Brianna plan to install a new tile floor in a classroom. Adam   [#permalink] 08 Mar 2018, 11:43
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