## andjie 2 years ago Can someone explain this for me step by step? Abby rows 10 km upstream and 10 km back in a total time of 3 hr. The speed of the river is 5 km/h. Find Abby’s speed in still water. @mark_o.

1. andjie

You found me lol

2. mark_o.

yeah im here now lol :D |dw:1354646559750:dw|

3. mark_o.

she row from starting point A to B then from B to A that is time from A to B + time from B to A = 3 hours

4. andjie

ok

5. mark_o.

time Tab + T ba = 3 (1) but distance d=velocity x time,. therefore t=d/v dAB dBA ------ + ------- =3 but distances dBA=dAB=10 km v v 10 10 ------- + ------ =3 v v but note that velocity of river is v=5 km/hr for upstream v= v+5 10 10 for down stream v= v-5, therefore ------- +------ = 3 v+5 v-5 you can algebra now ion finding v=?

6. mark_o.

i mean you can do the algebra now from this point ... :D

7. andjie

ummmm I am stuck

8. andjie

I am sorry lol

9. mark_o.

10/(v+5) + 10 /(v-5) =3 10(v-5) + 10(v+5) ------------------ =3 (v+5)(V-5)

10. mark_o.

do multiplication and addition to simplify the numerator and the denominator..:D

11. andjie

give me a sec

12. andjie

wow i suck cause I am lost

13. andjie

|dw:1354590455411:dw|

14. andjie

|dw:1354590757893:dw|

15. andjie

the v is throwing me off

16. mark_o.

10 10 -------- + ------- = 3 (v+5) (v-5) ? ------------------- =3 (v+5) (v-5)

17. andjie

20

18. andjie

|dw:1354591224584:dw|

19. mark_o.

for the further left, that is (v+5)(v-5) -----------= ? then mult by 10 (v+5)

20. mark_o.

then on the mid of it (v+5)(v-5) -----------= ? then mult by 10 (v-5)

21. andjie

|dw:1354591397442:dw|

22. mark_o.

10(v-5) + 10(v+5 ------------------- = 3 (v+5)(v-5)

23. andjie

|dw:1354591544810:dw|

24. andjie

ok give me a sec and let me figure this out

25. mark_o.

multiply the numerator then do addition on the denominator multiply them also

26. andjie

|dw:1354591871260:dw|

27. andjie

is that right

28. mark_o.

hhm where did you get 10-5 and 15+5 from? it should stay as 10( v-5)=? and 10(v+5)=?

29. andjie

I SUBTRACTED AND ADDED 10 FROM BOTH (V-5)(V+5)

30. andjie

10-5=5 AND 10+5=15

31. andjie

I just want to understand it

32. Hero

I guess you didn't like my explanation

33. andjie

no i asked you a question and you left

34. andjie

I just hate math and it takes me awhile to get it together

35. Hero

36. Hero

I left the room to help someone else with their question, but you should not assume that I had left.

37. mark_o.

it should stay as 10( v-5)=? and 10(v+5)=? 10( v-5)= 10v -50 is it ? and 10(v+5)= 10v +50 is it ?

38. mark_o.

ahh you have posted this before..yeah @andjie when we start coaching you dont assume that we had left .. :D

39. andjie

Thank you I am sorry

40. Hero

@mark_o. I am convinced you are doing this the hard way.

41. mark_o.

and for the denominator (v+5)(V-5)=?

42. mark_o.

haha i know..:D im sorry @Hero ...:D

43. Hero

Go check out my solution

44. mark_o.

where is that? lol... :D

45. Hero

I'll do anything to avoid a quadratic equation

46. Hero

Besides, I don't like when you get to a result where you have two solutions but have to discard one of them because it is negative.

47. mark_o.

i think andjie is just doing the refresher thing now.. to recall everything .. that was 7 years ago ? @ andjie?

48. andjie

9 almost ten years ago

49. Hero
50. andjie

wait I just had my high school reunion so it was 10 years ago lol

51. Hero

She's probably 28 years old

52. mark_o.

wow, almost 10 years ago? hmmm yeah this is a good refresher to you ... :D

53. andjie

29

54. Hero

I just posted a link to the solution

55. mark_o.

hhhm i cant open it, dont know why @Hero

56. andjie

I understand this better @hero hopefully I can do more like this

57. Hero

d = rt and let r = b ± w b = speed of the boat w = speed of the water current t1 = Upstream time t2 = Downsteam time 10 = 5t 2 = t1 t1 + t2 = 3 2 + t2 = 3 t2 = 3 - 2 t2 = 1 Upstream Formula d = rt1 d = (b - w)t1 Downsteam Formula: d = rt2 d = (b + w)t2 b - w = 5 Upstream 10 = 2(b - w) Downsteam 10 = (b + w) 10 = 2b - 2w 20 = 2b +2w 30 = 4b 30/4 = b 7.5 = b 10 = b + w 10 = 7.5 + w 10 - 7.5 = w 2.5 = w Therefore The speed of the boat was 7.5 km/h

58. mark_o.

ok this is good,, directly for the solutions and answer.... ;D

59. mark_o.

you did really avoid the quadratic equation .. :D

60. andjie

You guys are just too smart for me

61. Hero

I usually find ways to avoid it.

62. Hero

It's a personal goal of mine

63. andjie

lol

64. mark_o.

ok that is very good.... and andjie can copy this one to study and do for a second solution or alternate solution..........:D

65. andjie

Thank you @mark_o. you always look out for me

66. Hero

Well, back to watching Smallville. I'm trying to get to the end of the 10th season and it's taking forever.

67. andjie

Have fun and thank you for your help

68. mark_o.

ok YW,, tc now and have fun solving..........:D

69. mark_o.

thanks for doing the alternative solution, that was a good one :D @Hero...............:D

70. Hero

You're welcome. I have plenty alternative solutions up my sleeve.

71. Hero

If you need an alternative solution, cite me.