Question 1120492
together it takes dawn and deb 2 hr 55 min to sort recyclables. alone dawn would require 2 more hours then deb how long would it take deb to do the the job  alone
<pre>Let time Deb takes be D
Then time Dawn takes = D + 2
We then get: {{{matrix(1,3, 1/D + 1/(D + 2), "=", 1/(2&55/60))}}}
{{{matrix(1,3, 1/D +  1/(D + 2), "=", 1/(35/12))}}}
{{{matrix(1,3, 1/D + 1/(D + 2), "=", 12/35)}}}
35(D + 2) + 35D = 12D(D + 2) ------ Multiplying by LCD, 35D(D + 2)
{{{matrix(1,3, 35D + 70 + 35D, "=", 12D^2 + 24D)}}}
{{{matrix(1,11, 12D^2 - 46D - 70, "=", 0, "_____", 2(6D^2 - 23D - 35), "=", 0, "______", 6D^2 - 23D - 35, "=", 0)}}}
{{{matrix(1,3, 6D^2 - 30D + 7D - 35, "=", 0)}}}
6D(D - 5) + 7(D - 5) = 0
(D - 5)(6D + 7) = 0
Time Deb takes, or {{{highlight_green(matrix(1,4, D, "=", 5, hours))}}}         OR         {{{matrix(1,4, D, "=",  - 7/6, "(IGNORE)")}}}