## anonymous 3 years ago Rick can mop the floor in 5 minutes. Together Rick and Nancy can mop the floor in just 4 minutes. How long would it take Nancy to mop the floor alone?

1. anonymous

ricky's rate is $$\frac{1}{5}$$ i.e. he can do one fifth of the job in 5 minutes you want nancy's rate, lets call it $$r$$ then you know that $$4(\frac{1}{5}+r)=1$$

2. anonymous

you get $\frac{1}{5}+r=\frac{1}{4}$ $r=\frac{1}{4}-\frac{1}{5}$$r=\frac{1}{20}$

3. anonymous

6 minutes for rick, rick+nancy = 4. Nancy can do it in 2. that way 6 and 2 average to 4.

4. anonymous

so nancy's rate is $$\frac{1}{20}$$ of the job in one hour, would take nancy 20 hours working alone

5. anonymous

Yeah basically I summed it up but satellite73 has the more detailed answer if yours needed to be in fraction form :)

6. anonymous

the answer is not 2, and 4 is not the arithmetic average

7. anonymous

in fact that answer is clearly wrong, since if nancy can do it in two hours, how in the world will it take four hours for them to do it together??

8. anonymous

9. anonymous

20 hours working alone? it seems like they want minutes... or do I just convert it to minutes?

10. anonymous

like multiplied 60?