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