Question

I have a algebra 2 question I have no idea how to solve: You can type 1 page in 20 minutes. Your friend can type 1 page in 25 minutes. How long will it take you and your friend to type 60 pages if you work together?

Answer 1

you use the formula \[\huge \frac tx + \frac ty = 1\]
t is the total time it takes working together
x is the time it takes an individual to finsih alone
y is the time it takes for another individual to finish alone

first you need to get how long you can type 60 pages alone

you can typ 1 page in 20 minutes so you can time 60 pages in 1200 minutes.. make sense?

your friend can type 1 page in 25 minutes so he can type 60 pages in 1500 minutes

so \[\huge \frac{t}{1200} + \frac{t}{1500} = 1\]
solve for t


does that help?

Answer 2

or do you need more help?

Answer 3

THANK YOU SO MUCH!

Answer 4

welcome

Answer 5

how would you go about solving for t with the denominators different?

Answer 6

are you asking me or are you trying to give a hint?

Answer 7

you...

Answer 8

you multiply all terms by LCM for example you have \[\huge \frac t2 + \frac t3 = 1\]
you multiply all terms by the LCM which in this case is 6 so \[\huge \implies 3t + 2t = 6\]
add like terms
\[\huge 5t = 6\]
divide by 5
\[\huge t = \frac 65 \; \text{hours}\]

Answer 9

okay need more help

Answer 10

i accidentally added the two different denominators together whoops...
what comes after that.

Answer 11

oh thanks.

Answer 12

like i said you have \[\huge \frac{t}{1200} + \frac{t}{1500} = 1\]
the next step is to multiply all terms by the LCM

hint: the LCM for this one is 6,000

Answer 13

^btw.. these are minutes

Answer 14

okay so far i have \[\frac{ 54 }{ 600 }\]

Answer 15

1200t+1500t = 6000
2700t = 6000
t = 6000/2700
or 2.22

Answer 16

how did you get 54/600 again?

Answer 17

I crossed out the zeros in the fraction... it was \[\frac{ 540 }{ 6000 } \] but then i simplifyed it.

Answer 18

is this the only equation you can use to solve this type of problem or is this the one you know?

Answer 19

by equation i mean formula*

Answer 20

it actually comes from the formula \[\frac 1x + \frac 1y = \frac 1t\]

Answer 21

only one LOL. yeah i have a test tomorrow. I believe there is only one question like this. thank goodness

Answer 22

you can also use \[t = \frac{ab}{a+b}\]

Answer 23

by a and b i mean x and y respectively

Answer 24

when i first saw this question i thought system of equations. but i've only done Algebra I so far and will start Alegbra II this year so i haven't learned this.

Answer 25

anyway you ahve \[\huge \frac{1}{1200} + \frac{1}{1500} = 1\]
multiply all terms by 6,000
\[\huge \implies 5t + 4t = 6,000\]
combine like terms
\[\implies 9t = 6000\]
divide both sides by 9
\[\huge\implies t = 666.6\overline 6\]

Answer 26

^minutes

Answer 27

Thank you, that makes sense. :)

Answer 28

welcome