11 Grade Algebra

Joe and John are planning to paint a house together. John thinks that if he worked alone, it would take him 3 times as long as it would take Joe to paint the entire house. Working together, they can complete the job in 24 hours. How long will it take each of them, working alone to complete the job? Use the formula: Rate =

Let x = the time it takes Joe to complete the job.

Since, it takes John 3 times as long as Joe to complete the job:

3x = the time it takes John to complete the job.

The work they are trying to do is to paint 1 house.

Therefore, work = 1 for both Joe and John.

So, Joe’s equation would be: Rate =

& John’s equation would be: Rate =

So, their combined rate would be: +

The problem states, it takes 24 hours for them to paint 1, whole, house together –

If they can paint 1 whole house in 24 hour hours, they paint th of the house per hour, Rate = . Therefore, we can make the following combined rate equation:

+

We must now solve this for x.

So, we multiply their combined hourly rate by the LCD of 24x to clear the fractions and determine the time it would take them to complete 1 whole house, which gives you:

24x () = 24x ( + ) So,

x = +

Simplify each fraction on the right by cancelling any common factors

x = +

x = 24 + 8

x = 32 hours

Remember : Joe = x & John = 3x

So, it will take 32 hours for Joe to complete the job by himself.

Since, John = 3x, It will take John: 3(32) = 96 hours to complete the job by himself.

Kim and Kelly are planning to sew a quilt together. Kim thinks if she worked alone it would take her 4 times as long as it would take Kelly to sew the quilt by herself. Working together, they can complete the job in 2 hours. How long will it take each of them, working alone, to complete the job? Use the formula: Rate =

12) Jim and Mark can build a bookshelf in 9 hours when working together. It takes Jim 3 times longer to build a bookshelf by himself than it does Mark. How long will it take EACH of them, working alone, to build a bookshelf?