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