## anonymous 3 years ago If Jim Roller can paint a room in 3 hours while John Brush would take 5 hours, how long will they take if they work together?

1. anonymous
2. anonymous

a;1/8 hour b;8/15 hour c; 7/8 hours

3. anonymous

4. anonymous

What class is this?

5. anonymous

math

6. anonymous

I know, but what level of math?

7. anonymous

i need help

8. anonymous

You need to make a system of equations.

9. anonymous

Let, $$t$$ be the time it takes to paint the room. $$r$$ is the rate that Roller to paints it, $$b$$ is the rate that Brush paints it.

10. anonymous

We know that $3r = 5b$

11. anonymous

We also know that $(r+b)t = 3r = 5b$

12. anonymous

First solve for $$r$$ in terms of $$b$$ $3r=5b\implies r = \frac{5}{3}b$Now plug it into equation 2 $\left(\frac{5}{3}b+b\right)t=5b$

13. anonymous

Then solve for $$t$$.

shorcut way : 3*5/(3+5) = 15/8 long way :p v1+v2 = x/3 + x/5 = 8x/15 = x/(15/8) so, if they work together will take 15/8 hours