## anonymous one year ago Working together, 7 identical pumps can empty a pool in 6 hours. How many hours will it take 4 pumps to empty the same pool?

1. anonymous

@satellite73 can we take this one slow too?

2. anonymous

sure unit rate again

3. anonymous

So 7/6 will be how much 1 pump can empty a pool

4. anonymous

careful

5. anonymous

6. anonymous

isn't that what 7/6 finds?

7. anonymous

7 pumps take 6 hours, so 7 pumps do $$\frac{1}{6}$$ per hour

8. anonymous

oh okay

9. anonymous

how much does one pump do? don't multiply by 7, divide (like last time)

10. anonymous

1/42

11. anonymous

ok good now each pump does $$\frac{1}{42}$$ per hour, how much does 4 pumps do (this time multiply)

12. anonymous

4/42

13. anonymous

right

14. anonymous

or you can reduce to get $$\frac{2}{21}$$

15. anonymous

hmmmm did we do something wrong? my answer say 42/4 = 10 1/2

16. anonymous

you want to see how long it takes to do one job,

17. anonymous

solve $\frac{2}{21}T=1$ making $T=\frac{21}{2}$

18. anonymous

no we didn't do anything wrong, we just were not done yet we got the unit rate at $$\frac{2}{21}$$ but we need the total time

19. anonymous

ohhh okay

20. anonymous

they do 2/21 of a job per hour, takes 21/2 hours to do one job

21. anonymous

ohhh okay

22. anonymous

there may have been a quicker way to do this, but it is good to know how to get the unit rate so you can do all kinds of problems with it

23. anonymous

hmmm ok

24. anonymous

so do we now multiply by 4?

25. anonymous

no now we are done

26. anonymous

ohhh okay this is a different method i got it now

27. anonymous

we got the unit rate of $$\frac{1}{42}$$ that was pump per hour

28. anonymous

then we multiplied by 4 to get the rate for 4 pumps and got $$\frac{2}{21}$$

29. anonymous

ahhhh ic

30. anonymous

then we solved $\frac{2}{21}T=1$ the 1 being one pool

31. anonymous

if it was two pools it would have been $\frac{2}{21}=2$

32. anonymous

hmmm okay i think i understand now i'll review the last 2 problems we did a couple of times

33. anonymous

ok if you get stuck let me know

34. anonymous

i will thanks <333

35. anonymous

we can make one up and do it now if you like

36. anonymous

yes yes that would help even more

37. anonymous

see that they are not that hard and are largely the same

38. anonymous

yea

39. anonymous

you want me to make it up, or you want to?

40. anonymous

can u ?

41. anonymous

k they numbers might not come out real nice if i make it up off the top of my head, but no matter

42. anonymous

ok

43. anonymous

it takes 5 hours for 8 men to build one wall how long would it take 10 men to build 2 walls (sexist i now but whatever)

44. anonymous

first find the unit rate for one man let me know when you think you have it

45. anonymous

1/8 divided by 5 = 1/40

46. anonymous

yay!

47. anonymous

now the rate for 10 men

48. anonymous

1/40 * 10 = 10/40 = 1/4

49. anonymous

ok good now how long to build 2 walls

50. anonymous

1/4 * 2= 2/4= 1/2

51. anonymous

aw damn we were doing so well

52. anonymous

oh crap...

53. anonymous

not going to take half an hour !

54. anonymous

now we need to go slow either we solve $\frac{1}{4}T=2$

55. anonymous

ohhhhhh yeaaaa thats right so 8

56. anonymous

yup

57. anonymous

ok i'll keep practicing this

58. anonymous

almost got it 100% thanks satellite

59. anonymous

ok, i think it is getting easier though right? first part went quick

60. anonymous

yw