I have an equation I would like solving.

Question

I need to solve the following problem

Decorator A is painting a large wall. At her current rate, she will complete the wall in 1 hour and 40 minutes.

Decorator B is painting a similar wall, although he is a little faster and will likely complete the wall in 1 hour.

Decorator C is painting a similar wall too, but he is slower and will complete the wall in 2 hours.

Assuming Decorators A, B and C and 6 more decorators, three of which are as fast as B and 3 of which are as fast as C collaborated on the same wall, how long would they complete a wall together?

However, I don't know how to set up a proper model for this question. Can someone point me in the right direction?

Answer 1

What percentage of a wall would they paint together in an hour?

Each A-class painter would paint $\frac{3}{5}$ of a wall, since he would need $\frac{5}{3}$ hour (or 1h40) for a full wall.

Each B-class painter would paint a full wall.

Each C-class would paint $\frac12$ of a wall.

So, all the nine painters would paint, in an hour:

$\frac35+4\times1+4\times\frac12=\frac{33}{5}$ of a wall.

Now, how much time to finish a wall?

Answer 2

Hint: Think about: How much of a wall does each painter cover in a minute?