Question 1198737

It takes Calvin 2 hours longer to complete the promotional logo for a male business entrepreneur than it takes Francesca. The two of them work together for 3 hours then Francesca left, and Calvin finished the job in 1 hour. How long would it take each of them, working alone, to finish the job?
<pre>Let time Francesca takes to do the job, alone, be F
Then time Calvin takes to do the job, alone, is F + 2
So, Franxesca can do {{{1/F}}} of job in 1 hour, while Calvin can do {{{1/(F + 2)}}} of job in 1 hour
Together, they can do {{{1/F + 1/(F + 2)}}} of job in 1 hour
Since they both worked for 3 hours before Calvin completed the unfinished work in 1 hour, we get the following equation
for the entire JOB: {{{matrix(1,3, 3(1/F + 1/(F + 2)) + 1(1/(F + 2)), "=", 1)}}}   
                            {{{matrix(2,3, 3/F + 3/(F + 2) + 1/(F + 2), "=", 1, 3/F + 4/(F + 2), "=", 1)}}}
                               3(F + 2) + 4F = F(F + 2) ----- Multiplying by LCD, F(F + 2)
                                  {{{matrix(4,3, 3F + 6 + 4F, "=", F^2 + 2F, 7F + 6, "=", F^2 + 2F, 0, "=", F^2 + 2F - 7F - 6, 0, "=", F^2 - 5F - 6)}}}
                                           0 = (F - 6)(F + 1)
                                       F - 6 = 0     OR      F + 1 = 0
<font size = 4><font color = blue><b>Time Francesca takes to do the job, alone</font></font></b>, or F = <font size = 4><font color = blue><b>6 hours

Time Calvin takes to do the job, alone:</font></font></b> F + 2 = 6 + 2 = <font size = 4><font color = blue><b>8 hours</font></font></b></pre>