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My friend and I both have the same math homework one day. I work at a rate of p problems per hour and it takes me t hours to finish my homework. My friend works at a rate of 2p-6 problems per hour and it only takes him t-1 hours to finish his homework. What is the most number of problems I can do per hour?

 Dec 6, 2020
 #1
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+1

pt  = (2p - 6)(t - 1)

 

pt  = 2pt -2p -6t + 6

 

pt - 2p -6t + 6    =  0

 

pt - 2p =  6t - 6

 

p ( t - 2)  =  6t - 6

 

p =   (6t -6)

       ______

         t  - 2

 

t         p

3      12

4       9

8       7

......

 

Look  at  the graph here  ....  https://www.desmos.com/calculator/knrv5knjuc

 

Letting    t   =  x     and y  = p.....note  that p will be maximized  when  t   =  x    = 3

 

And when   t  = 3     then p  =12  =   the greatest number of problems you can work in one hour

 

 

 

cool cool cool

 Dec 6, 2020

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