Answer: The time taken by Jennifer to complete this job on her own is 6 hours.
Step-by-step explanation:
Let x be the hour taken by Jennifer in the entire work when she works alone,
⇒ The time taken by Carl when he works alone = (x - 3) hours ( Because, Carl can paint a room 3 hours faster than Jennifer can ),
The Work done by Jennifer in one day = [tex]\frac{1}{x}[/tex]
While, the The Work done by Carl in one day = [tex]\frac{1}{x-3}[/tex]
The total work done by both in one day = [tex]\frac{1}{x}+\frac{1}{x-3}[/tex]
According to the question,
If they work together, they can complete the job in 2 hours.
⇒ The total work done by both in one day when they work together = [tex]\frac{1}{2}[/tex]
[tex]\implies \frac{1}{x}+\frac{1}{x-3} = \frac{1}{2}[/tex]
[tex]\frac{x-3+x}{x^2-3x}=\frac{1}{2}[/tex]
[tex]\frac{2x-3}{x^2-3x}=\frac{1}{2}[/tex]
[tex]4x-6=x^2-3x[/tex]
[tex]x^2-7x+6=0[/tex]
[tex]x^2-6x-x+6=0[/tex]
[tex]x(x-6)-1(x-6)=0[/tex]
[tex](x-1)(x-6)=0[/tex]
If x-1 = 0 ⇒ x = 1 ( But the time taken by carl = 1-3 = -2, which can not be possible ),
If x-6=0 ⇒ x = 6,
Hence, the time taken by Jennifer to complete this job on her own = 6 hours.
