## dumbsearch2 2 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. satellite73

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. satellite73

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

3. gianarpt

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

4. satellite73

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

5. gianarpt

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

6. satellite73

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

7. satellite73

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. dumbsearch2

9. dumbsearch2

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

10. dumbsearch2

like multiplied 60?