## anonymous one year ago Molly can prepare a report in 6 hours. Jere can prepare a report in only 4 hours. Which of the following can be used to determine the amount of time it would take for Molly and Jere to prepare a report together?

1. anonymous

1 over 6 plus 1 over x equals 1 over 4 1 over x plus 1 over 4 equals 1 over 6 1 over 4 plus 1 over 6 equals x over 10 1 over 6 plus 1 over 4 equals 1 over x

2. jim_thompson5910

Hint M = time it takes for molly to prepare the report (with no help from others) J = time it takes for Jere to prepare the report (with no help from others) $\large \frac{1}{\text{Molly's Time}}+\frac{1}{\text{Jere's Time}} = \frac{1}{\text{Time if they work together}}$ $\large \frac{1}{M}+\frac{1}{J} = \frac{1}{\text{Time if they work together}}$ I'll let you finish

3. anonymous

So would it be D?

4. anonymous

@jim_thompson5910

5. jim_thompson5910

correct

6. anonymous

7. jim_thompson5910

sure

8. anonymous

9. anonymous

Nathaniel can weld a railing in 75 minutes. Brenda can weld a railing 25 minutes faster. If they work together, how many minutes does it take them to weld the railing?

10. anonymous

25 minutes 30 minutes 50 minutes 150 minutes

11. jim_thompson5910

same idea, just different numbers

12. jim_thompson5910

$\Large \frac{1}{75} + \frac{1}{25} = \frac{1}{x}$ x = time in minutes it takes them to do the job together

13. anonymous

sO 50 minutes ?

14. jim_thompson5910

oh wait, I have the wrong equation

15. anonymous

ok:)

16. jim_thompson5910

Nathaniel can weld a railing in 75 minutes. Brenda can weld a railing 25 minutes faster. so Brenda takes 75-25 = 50 minutes $\Large \frac{1}{75} + \frac{1}{50} = \frac{1}{x}$ isolate x

17. anonymous

how do I do that?

18. jim_thompson5910

what does 1/75 + 1/50 turn into?

19. jim_thompson5910

add them up like normal fractions

20. anonymous

150 is the gcf

21. jim_thompson5910

yes

22. jim_thompson5910

well LCD actually but yeah

23. anonymous

2x+3x/150x=150/150x

24. anonymous

So 30 min?

25. jim_thompson5910

yes x = 30

26. anonymous

Yayyy!!!! Thank-you!

27. anonymous

Up for another?

28. jim_thompson5910

I'll help with one last one

29. anonymous

It takes Harland 15 minutes to rake all leaves in the front yard. If Trudy scatters the leaves while Harland rakes, it takes him 20 minutes to rake the leaves. How many minutes does it take Trudy to scatter all the leaves?

30. anonymous

Deal:)

31. anonymous

5 minutes 12 minutes 45 minutes 60 minutes

32. anonymous

I'm thinking 60 minutes

33. jim_thompson5910

what does 1/20 + 1/15 add up to?

34. anonymous

35. anonymous

Um the LCD is 60

36. anonymous

4x/60x +3x/6x =60/60x

37. jim_thompson5910

oh I have a typo, let me fix it

38. anonymous

kk

39. jim_thompson5910

the 1/y should have been negative

40. anonymous

Ok :)

41. jim_thompson5910

sorry another typo, but I'm sure this time it's correct x = time it takes for Harland to rake all the leaves (without Trudy in the way) y = time it takes Trudy to scatter all the leaves (without Harland in the way) z = time it takes Harland to rake all the leaves with Trudy scattering the leaves at the same time $\Large \frac{1}{x} - \frac{1}{y} = \frac{1}{z}$ $\Large \frac{1}{15} - \frac{1}{y} = \frac{1}{20}$ $\Large \frac{1}{15} - \frac{1}{y} + \frac{1}{y} = \frac{1}{20} + \frac{1}{y}$ $\Large \frac{1}{15} = \frac{1}{20} + \frac{1}{y}$ $\Large \frac{1}{15} - \frac{1}{20} = \frac{1}{20} + \frac{1}{y} - \frac{1}{20}$ $\Large \frac{1}{15} - \frac{1}{20} = \frac{1}{y}$

42. jim_thompson5910

not sure why I'm being so careless lol

43. anonymous

so would the answer be 60?

44. anonymous

It's fine<3

45. jim_thompson5910

anyways, you had the right idea in saying 1/15 - 1/20 that leads to 1/60 so y = 60

46. anonymous

Thanks so much for all your help:)))

47. jim_thompson5910

no problem