Working together, two workers can finish a concrete floor in 40 minutes. Working alone, the worker with the smaller machine is 25 minutes longer than the worker with the large machine. Approximate to the nearest minute the time it will take the worker with the larger machine, working alone, to finish the job.
+130516 Let the number of minutes that the faster worker takes to do the job = x
Let the number of minutes that the slower worker takes = x +25
So each minute, the faster worker does 1/x of the job and the slower worker does 1/[x + 25] of the job.........and Rate * Time = Amount of the job done.....so we have
(1/x)(40) + (1/ [ x + 25])(40) = 1
40/ [x] + 40/[x + 25] = 1
[40(x + 25) + 40x] / [x (x + 25) = 1 multiply both sides by x(x + 25)
80x + 1000 = x^2 + 25x rearrange
x^2 - 55x - 1000 = 0
The graph of this equation here.....https://www.desmos.com/calculator/pypr5mfqrr
shows that the positive solution for x occurs at about 69.41 hours = about 69 hrs 24.6 min = 69 hrs 25 min ......and this is how long the faster worker takes to complete the job rounded to the nearest minute
