Question

Hannah can paint a room in 15 hours. Destiny can paint the same room in 12 hours. How long does it take for both Hannah and Destiny to paint the room it they are working together?

Answer 1

To start to solve this question, we need to first find how much of the task, painting the room, each one can do in one hour. To do this, we take the reciprocal of the amount of time that it takes for them to paint the whole room.

Using this knowledge, we get:

Hannah - $\frac{1}{15}$ of the room per hour

Destiny - $\frac{1}{12}$ of the room per hour

Now, to find how much time it will take for them to paint the entire room, let's set up a variable, t, that will represent this quantity. We know that the pair has finished if they have painted the entire room, or '1.' Now we can set up an equation.

Since we know that the combined hourly rate will be the sum of Hannah and Destiny's hourly rates, to find how fast they finish '1' job, we need to multiply by our unknown, t. Our equation becomes:

($\frac{1}{15}$ + $\frac{1}{12}$) t = 1

Simplifying, we get:

$\frac{9}{60}$ t = 1

Solving for t, we get:

t = 1 · $\frac{60}{9}$ = $\frac{60}{9}$

That means that they will finish the job in 6 2/3 hours, if painting together.