Question 685827
A and B working together can finish a job in T days.  If A works alone and completes the job, he will take T + 5 days.  If B works alone and completes the same job, he will take T + 45 days.  What is T?
<pre>
Their combined rate is 1 job per T days or {{{(1_job)/(T_days)}}} or {{{1/T}}}{{{job/day}}}

A's rate is 1 job per T+5 days or {{{(1_job)/(T+5_days)}}} or {{{1/(T+5)}}}{{{job/day}}}

B's rate is 1 job per T+45 hours or {{{(1_job)/(T+45_days)}}} or {{{1/(T+45)}}}{{{job/days}}}

The equation comes from {{{(matrix(4,1,

"A's", rate, in, "job/days"))}}} + {{{(matrix(4,1,

"B's", rate, in, "job/days"))}}} = {{{(matrix(5,1,

Their, combined, rate, in, "job/days"))}}}

                                     {{{1/(T+5)}}} + {{{1/(T+45)}}} = {{{1/T}}}

Multiply through by LCD = T(T+5)(T+45) and solve.  You'll get T = 15 days.

Edwin</pre>