Question

Keianaka and Christopher are participating in a volunteer project painting homes for elderly people in their neighborhood. Keianaka and her team can paint one house in 60 minutes. Christopher and his team can paint one house in 80 minutes. If they joined their teams, how quickly could they paint one house?

Answer 1

The K-team can paint a whole house in 60 minutes (super fast!!!). How much of a house can the team paint in 1 minute?  The K-team can paint 1/60 of a house per minute.

The C-team can paint a whole hose in 80 minutes. How much of a house can the team paint in 1 minute? The C-team can paint 1/80 of a house per minute.

Suppose both teams paint for the same amount of time --  call the time t (minutes).

Combine the work they do to paint 1 whole house:

$\frac{1}{60}t+\frac{1}{80}t=1$

Multiply all the terms by the Least Common Denominator,  LCD = 240.

$240(\frac{1}{60})t+240(\frac{1}{80})t=240$

Now, can you finish it? By the way, the answer is not a whole number!  Hint: it will be between 30 and 40 minutes.