andjie
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.
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andjie
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You found me lol
mark_o.
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yeah im here now lol :D
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mark_o.
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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
andjie
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ok
mark_o.
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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=?
mark_o.
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i mean you can do the algebra now from this point ... :D
andjie
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ummmm I am stuck
andjie
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I am sorry lol
mark_o.
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10/(v+5) + 10 /(v-5) =3
10(v-5) + 10(v+5)
------------------ =3
(v+5)(V-5)
mark_o.
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do multiplication and addition to simplify the numerator and the denominator..:D
andjie
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give me a sec
andjie
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wow i suck cause I am lost
andjie
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andjie
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andjie
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the v is throwing me off
mark_o.
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10 10
-------- + ------- = 3
(v+5) (v-5)
?
------------------- =3
(v+5) (v-5)
andjie
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20
andjie
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mark_o.
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for the further left, that is
(v+5)(v-5)
-----------= ? then mult by 10
(v+5)
mark_o.
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then on the mid of it
(v+5)(v-5)
-----------= ? then mult by 10
(v-5)
andjie
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mark_o.
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10(v-5) + 10(v+5
------------------- = 3
(v+5)(v-5)
andjie
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andjie
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ok give me a sec and let me figure this out
mark_o.
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multiply the numerator then do addition
on the denominator multiply them also
andjie
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andjie
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is that right
mark_o.
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hhm where did you get 10-5 and 15+5 from?
it should stay as 10( v-5)=? and 10(v+5)=?
andjie
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I SUBTRACTED AND ADDED 10 FROM BOTH (V-5)(V+5)
andjie
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10-5=5 AND 10+5=15
andjie
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I just want to understand it
Hero
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I guess you didn't like my explanation
andjie
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no i asked you a question and you left
andjie
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I just hate math and it takes me awhile to get it together
Hero
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Well, I just answered your question
Hero
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I left the room to help someone else with their question, but you should not assume that I had left.
mark_o.
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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 ?
mark_o.
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ahh you have posted this before..yeah @andjie when we start coaching you dont assume that we had left .. :D
andjie
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Thank you I am sorry
Hero
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@mark_o. I am convinced you are doing this the hard way.
mark_o.
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and for the denominator
(v+5)(V-5)=?
mark_o.
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haha i know..:D im sorry @Hero ...:D
Hero
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Go check out my solution
mark_o.
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where is that? lol... :D
Hero
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I'll do anything to avoid a quadratic equation
Hero
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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.
mark_o.
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i think andjie is just doing the refresher thing now.. to recall everything .. that was 7 years ago ? @ andjie?
andjie
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9 almost ten years ago
andjie
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wait I just had my high school reunion so it was 10 years ago lol
Hero
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She's probably 28 years old
mark_o.
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wow, almost 10 years ago? hmmm yeah this is a good refresher to you ... :D
andjie
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29
Hero
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I just posted a link to the solution
mark_o.
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hhhm i cant open it, dont know why @Hero
andjie
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I understand this better @hero hopefully I can do more like this
Hero
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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
mark_o.
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ok this is good,, directly for the solutions and answer.... ;D
mark_o.
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you did really avoid the quadratic equation .. :D
andjie
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You guys are just too smart for me
Hero
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I usually find ways to avoid it.
Hero
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It's a personal goal of mine
andjie
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lol
mark_o.
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ok that is very good.... and andjie can copy this one to study and do for a second solution or alternate solution..........:D
andjie
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Thank you @mark_o. you always look out for me
Hero
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Well, back to watching Smallville. I'm trying to get to the end of the 10th season and it's taking forever.
andjie
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Have fun and thank you for your help
mark_o.
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ok YW,, tc now and have fun solving..........:D
mark_o.
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thanks for doing the alternative solution, that was a good one :D
@Hero...............:D
Hero
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You're welcome. I have plenty alternative solutions up my sleeve.
Hero
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If you need an alternative solution, cite me.