Virginia Can Complete Her Company's Monthly Report In 5 Hour Les…

virginia can complete her company’s monthly report in 5 hour less time than Carl. If they work together, the report will take them 6 hour to finish. How long would it take Virginia working alone?

x=Carl’s
x-5=Virginia’s

1/x+1/x-5=1/6  [LCD: (x) (x-5) (6)]
6x-30+6x=x^2-5x
-x^2+17x-30=0
x^2-17x+30x=0
(x-5)(x-2)=0
x={15,2}

Answer: Virginia will take 10 hours to complete her company’s monthly report. 

Sol.:

1/2+1/(2-5)=1/6
1/6=1/6
(INCORRECT because it is stated in the problem that Virginia would take 5 hours less than the time of Carl and it is impossible to have 2 hours of working hours less than five. That would equate to negative.) So x=2 is not applicable to the problem.

1/15+1/(15-5)=1/6
1/15+1/10=1/6
2/30+1/30=1/6
1/6=1/6

The real answer is 10 in which we subtracted it from Carl’s working hours which is 15. (x=15)

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