Question

How would I solve this? It's a rational expression, I think.

Answer 1

\[\frac{ 1 room }{ 3x } + \frac{ 1 room }{ x } = \frac{ 1 room }{ 2 hours }\]

Answer 2

That's quite an unusual expression! I think you could safely cross "room" out from each term and solve the resulting simpler equation:\[\frac{ 1 }{ 3x }+\frac{ 1 }{ x }=\frac{ 1 }{ 2 }\]
Please identify the LCD and multiply every term by that. Solve the resulting equation for x. Note that x can NOT = 0. (Why not?)

Answer 3

Would 1/x become 3 / 3x?

Answer 4

YES!

Answer 5

It is not 3x - ur question said "3 hours faster" not "3 times faster" right?

Answer 6

Dave: Where'd that come from?

Answer 7

Hahahaaa sorry - what happened to the question itself? Or was I seeing things now O^O

Answer 8

OH. I posted the question but deleted it because I thought I'd solved it. D: (Sorry I disappeared for a second, I was solving another question.)

Answer 9

here is the original word problem:

Answer 10

It should be x + 3 then! Oops, my bad!

Answer 11

1/3+x + 1/x = 1/2

Answer 12

:) glad 2 know dat i wasnt seeing things lol so u need 2 set up ur eqn again. there should be two eqns....

Answer 13

Hahahaaa nevermind...u already skipped the second eqn n did the substitution...

Answer 14

..what? I'm confused now.

Answer 15

@mathmale

Answer 16

I will let others 2 help u finish this one...but i dont think 1/2 on the right hand side is correct....good luck!

Answer 17

It is! According to the problem, they can complete one room in 2 hours.

Answer 18

So perhaps it should be 2 instead of 1/2? :)

Answer 19

Noo, 1 room, in two hours. That's how the equation is set up.

Answer 20

This isn't the first time I've done questions like this, but usually the x is on the other side of the equal sign because i'm asked to find how long it will take two of them to do one thing. But this question is backwards.

Answer 21

Yup its backwards indeed. I still think it should be 2 hrs on the right but plz feel free to ask others to confirm :)

Answer 22

Write the equation y - 2 = 4(x + 5) in standard form. (Points : 1)
4x + y = 7
4x - y = 3
4x - y = -22

Answer 23

Can you not? ^

Answer 24

Post your own question, please. e.e

Answer 25

I believe I have a solution: Jennifer can paint the whole house (complete 1 job ) in 6 hours.

I started out writing work rates. If Carl can paint 1 room in 3 hours less than Jennifer can, his job completion rate would then be
\[\frac{ 1 room }{( x-3) hours }\]
where x = # of hours Jennifer requires to paint the room and x-3 = # of hours Carl requires to do the same.
Jennifer's job completion rate would then be
\[\frac{ 1 room }{( x) hours }\].
Since we now have a job completion rate for both individuals, we can find the fraction of the complete job that either does by multiplying his or her job completion rate by the number of hours worked.

Answer 26

In 2 hours, the fraction of the job done by Carl will be\[\frac{ 1 }{ x }(2).\] \[\frac{ 1 }{ x-3 }(2)\]
and that by Jen
\[\left( \frac{ 1 }{ x } \right)(2).\]

Answer 27

Sum up these two fractions. Equate the result to "1 job."
\[(\frac{ 1 }{ x-3 }+\frac{ 1 }{ x })(2)=1.\]
Eliminating the fractions results in (2x-3)=x(x-3).

Anyone care to complete the solution for x?
Initially I stated that x=6 hours, but 6 is not a solution of this final equation.

Answer 28

@mathmale You are GREAT in your explanation!!! Wish I could give u more than one medal!!! I dont think the Q requires an actual solution but a step-by-step description only; which u have already done! GREAT job!!

@Jaylikescookies - I apologize: I did the math in my head w/o writing it down. So u are RIGHT n I was wrong. I apologize for my mistake n me bugging u earlier today :)

Answer 29

Many thanks, Dave!
@jaylikescookes : Thanks for sharing such an interesting problem with the rest of us.