If jen can paint a room in 7 hours and jen and keith can paint the room in 4 hours. how long will it take keith to paint the room alone?
1/k + 1/7 = 1/4
Now just solve for k.
Is the answer x= 28/3
To find out how long it will take Keith to paint the room alone, we need to use the concept of work.
Let's assume that the amount of work required to paint the room is 1 (you can think of it as a unit).
If Jen can paint the room in 7 hours, it means that Jen can do 1/7th of the work in 1 hour, because 1 hour is 1/7th of 7 hours.
If both Jen and Keith can paint the room in 4 hours, it means that together they can do 1/4th of the work in 1 hour, because 1 hour is 1/4th of 4 hours.
Now, let's subtract the work done by Jen alone from the work done by Jen and Keith together to find the work done by Keith alone:
Work done by Keith alone = Work done by Jen and Keith together - Work done by Jen alone
Work done by Keith alone = 1/4 - 1/7
To calculate this, we need to find a common denominator for both fractions, which is 28.
Work done by Keith alone = (7/28) - (4/28) = 3/28
So, Keith can do 3/28th of the work in 1 hour.
To find out how long it will take Keith to paint the room alone, we need to calculate the reciprocal of the fraction 3/28. This can be done by flipping the fraction, which gives us 28/3.
Therefore, it will take Keith approximately 9.33 hours (28 divided by 3) to paint the room alone.