Question

Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can complete the job in 2 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jennifer to complete this job on her own.

Answer 1

If Carl can complete it 3 hrs faster then Jennifer that means when they do it together its only 2 hrs so you would multiply 3 x 2 which then you would get 6 hrs. 

Answer 2

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 = $\frac{1}{x}$

While, the The Work done by Carl in one day = $\frac{1}{x-3}$

The total work done by both in one day = $\frac{1}{x}+\frac{1}{x-3}$

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 = $\frac{1}{2}$

$\implies \frac{1}{x}+\frac{1}{x-3} = \frac{1}{2}$

$\frac{x-3+x}{x^2-3x}=\frac{1}{2}$

$\frac{2x-3}{x^2-3x}=\frac{1}{2}$

$4x-6=x^2-3x$

$x^2-7x+6=0$

$x^2-6x-x+6=0$

$x(x-6)-1(x-6)=0$

$(x-1)(x-6)=0$

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.