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Mathematics 10 Online
OpenStudy (anonymous):

What is the product of: 16t^3/2t+4 * t+2/8t.

OpenStudy (anonymous):

okay thank you. But what did I need to do? Cross multiply or, cancel out.... can u explain

OpenStudy (anonymous):

okay, the answer you gave isn't one of my answers

jimthompson5910 (jim_thompson5910):

Luis_Rivera, you're close, but you'll have two sets of '2' cancel as well

OpenStudy (anonymous):

please help!! I wanna be able to finish this test quick!! I wanna do something else other than Virtual School!!

OpenStudy (anonymous):

is t^2?

jimthompson5910 (jim_thompson5910):

yeah that's what you'll be left with

OpenStudy (anonymous):

yay. can you help me with something else?

jimthompson5910 (jim_thompson5910):

ok one more

OpenStudy (anonymous):

urgh... I have like a lot more than one... but I'll choose the hardest one for me...

OpenStudy (anonymous):

urgh... I have like a lot more than one... but I'll choose the hardest one for me... What is the sum of\[\frac{8g }{ g^5 } +\frac{ 7-g }{ g^5 }\]

jimthompson5910 (jim_thompson5910):

the denominators are the same so you can add the numerators and place them over the common denominator

OpenStudy (anonymous):

umm... what does that mean? i'm not good with math terms.

jimthompson5910 (jim_thompson5910):

the denominator is the lower portion of the fraction

jimthompson5910 (jim_thompson5910):

the numerator is the upper portion

OpenStudy (anonymous):

okay really quick:

OpenStudy (anonymous):

if you had 60 = 12t + 10t how would you solve for t?

jimthompson5910 (jim_thompson5910):

combine the 12t and the 10t to get _____

OpenStudy (anonymous):

22t,

jimthompson5910 (jim_thompson5910):

good, so 60 = 22t

jimthompson5910 (jim_thompson5910):

then you divide both sides by 22 to isolate t 60/22 = t

jimthompson5910 (jim_thompson5910):

make sure you reduce as much as possible

OpenStudy (anonymous):

ohhh so, 60/22 Is the fraction since it cant be divided?

jimthompson5910 (jim_thompson5910):

well you would reduce to get 30/11

jimthompson5910 (jim_thompson5910):

so t = 30/11

OpenStudy (anonymous):

umm... I'm not sure that works with my equation... umm... I have 2=2t/5 + 2t/6

jimthompson5910 (jim_thompson5910):

ok notice the denominators are 5 and 6

jimthompson5910 (jim_thompson5910):

they are not the same, so you cannot add the fractions right away

OpenStudy (anonymous):

yes

jimthompson5910 (jim_thompson5910):

so you need to find the LCD

OpenStudy (anonymous):

i know, i have to find the lcm and then I have to multiply it by the lcm, (or lcd) to both sides, then that's where I think i went wrong.

jimthompson5910 (jim_thompson5910):

the LCD is 30

OpenStudy (anonymous):

yes, then I got, 60 =

jimthompson5910 (jim_thompson5910):

good, what did you get for the right side

OpenStudy (anonymous):

60 = 60t/5 + 60t/6

OpenStudy (anonymous):

oh yeah, is the first equation, 7/g^4

jimthompson5910 (jim_thompson5910):

ok i see how you got 60 = 12t + 10t

jimthompson5910 (jim_thompson5910):

the answer to 60 = 12t + 10t is t = 30/11 the answer to 2=2t/5 + 2t/6 is also t = 30/11 so that shows evidence the two are equivalent (and it turns out they are)

OpenStudy (anonymous):

but that doesn't work with my question.

OpenStudy (anonymous):

want me to post the question?

jimthompson5910 (jim_thompson5910):

ok what is the original question

jimthompson5910 (jim_thompson5910):

yes please

OpenStudy (anonymous):

Shannon and Macie are raking leaves to earn some money. Shannon can rake 2 lawns that are about the same size in 5 hours. Macie can rake 2 lawns that are about the same size in 6 hours. How long would it take both girls to work together to rake 2 lawns? Write and solve an equation for this situation. Explain how to set up the equation, using w = rt.

jimthompson5910 (jim_thompson5910):

so you're really solving the equation 1/5 + 1/6 = 1/t for t

jimthompson5910 (jim_thompson5910):

ignore the 2 from the two lawns think of doing 2 lawns as one complete job

OpenStudy (anonymous):

that's not what it says to do in my lesson though... but okay. let's work your system first and see if it works

jimthompson5910 (jim_thompson5910):

what's the LCD

OpenStudy (anonymous):

its still 30

jimthompson5910 (jim_thompson5910):

yes but keep in mind there's a t in the denominator as well

OpenStudy (anonymous):

but the t's not supposed to be in the 'w' part

jimthompson5910 (jim_thompson5910):

ok think of it like this

jimthompson5910 (jim_thompson5910):

Shannon can rake 2 lawns that are about the same size in 5 hours or put another way Shannon can do one job in 5 hours where a complete job is considered to be raking 2 lawns of the same size

jimthompson5910 (jim_thompson5910):

so for Shannon only, her work/rate/time equation is w = rt 1 = r*5 solve for r to get r = 1/5

jimthompson5910 (jim_thompson5910):

so her rate is 1/5 of a job per hour

OpenStudy (anonymous):

Can I just put something out there: I think it's 3 hours. (or approximately three hours)

jimthompson5910 (jim_thompson5910):

similarly for Macie, her equation is w = rt 1 = r*6 r = 1/6 so Macie's rate is 1/6 of a job per hour

jimthompson5910 (jim_thompson5910):

combined, their total rate is 1/5 + 1/6 jobs per hour

jimthompson5910 (jim_thompson5910):

so if that's the 'r' in w = rt, then w = rt w = (1/5 + 1/6)*t 1= (1/5 + 1/6)*t now solve for t

OpenStudy (anonymous):

uhhh... you got me confused actually... so umm... gimme a minute

jimthompson5910 (jim_thompson5910):

ok

OpenStudy (anonymous):

wouldn't you still get 30/11 as an answer?

jimthompson5910 (jim_thompson5910):

you would

OpenStudy (anonymous):

but.. how does that work for the question?

jimthompson5910 (jim_thompson5910):

which is 2.73 hours roughly

OpenStudy (anonymous):

ohhhhhhhh!!! So the calculator was right!!! :D

jimthompson5910 (jim_thompson5910):

that's how long it would take for them to work together

jimthompson5910 (jim_thompson5910):

assuming one doesn't hinder the other

OpenStudy (anonymous):

haha! okay, can you help me finish my test really quick? I have three questions left. :)

OpenStudy (anonymous):

pleeeease

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