SOLUTION: 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 l

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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?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Calvin 1%2F%28x%2B2%29
Francesca 1%2Fx

Together for 3 hours and then Calvin 1 more hour
%281%2F%28x%2B2%29%2B1%2Fx%293%2B%281%2F%28x%2B2%29%29%2A1=1

3%281%2F%28x%2B2%29%2B1%2Fx%29%2B1%2F%28x%2B2%29=1
3%2F%28x%2B2%29%2B3%2Fx%2B1%2F%28x%2B2%29=1
4%2F%28x%2B2%29%2B3%2Fx=1
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4x%2B3%28x%2B2%29=x%28x%2B2%29
4x%2B3x%2B6=x%5E2%2B2x
5x%2B6=x%5E2
x%5E2-5x-6=0
%28x-6%29%28x%2B1%29=0
highlight%28x=6%29---------time for Francesca alone to do the job.
Calvin would need 8 hours to do the same job alone.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

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?
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%2FF of job in 1 hour, while Calvin can do 1%2F%28F+%2B+2%29 of job in 1 hour
Together, they can do 1%2FF+%2B+1%2F%28F+%2B+2%29 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:    
                            
                               3(F + 2) + 4F = F(F + 2) ----- Multiplying by LCD, F(F + 2)
                                  
                                           0 = (F - 6)(F + 1)
                                       F - 6 = 0     OR      F + 1 = 0
Time Francesca takes to do the job, alone, or F = 6 hours

Time Calvin takes to do the job, alone: F + 2 = 6 + 2 = 8 hours