# Two friends are painting a living room. Ken can paint it in 6 hours working alone. If Barbie works alone, it will take her 8 hours. How long will it take working together?

##### 3 Answers

Let,the total work is of

So,ken does

So,in

Now,Barbie does

So,in

Let,after working

So, in

Clearly,

Or,

So,

Detailed solution given so that you can see where everything comes from.

#### Explanation:

People work at different rates. So the time taken by different people to complete a set amount of work will also be different. This is what we need to model

Let the total amount of work required to complete the task be

Let Ken's work rate per hour be

Let Barbie's work rate per hour be

Let the total time **working together** be

If Ken works on his own he can complete the whole task in 6 yours

So

If Barbie works on her own she can complete the whole task in 8 hours

Using the above method

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider

Factor out the

#### Explanation:

First find out what fraction of the task they would each complete in

Ken will finish

Barbie will finish

If they work together, in one hour they will finish:

So to complete the whole task

This simplifies to

Which is easier given as

or