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?
+128473 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
