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.

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 =
`(1)/(x)`

While, the The Work done by Carl in one day =
`(1)/(x-3)`

The total work done by both in one day =
`(1)/(x)+(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 =
`(1)/(2)`

`\implies (1)/(x)+(1)/(x-3) = (1)/(2)`

`(x-3+x)/(x^2-3x)=(1)/(2)`

`(2x-3)/(x^2-3x)=(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.