anonymous
  • anonymous
I need help someone. Can someone please help me?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Write a word problem describing the time it takes to complete an activity individually and with a friend. For example, if John takes 2 hours to mow his lawn and it takes his sister Maria 4 hours to mow the same lawn, how long would it take John and Maria to mow the lawn together? Write a rational equation based upon the word problem you created. The rational equation based upon the scenario above would be \[\frac{ 1 }{ 2 } + \frac{ 1 }{ 4 } = \frac{ 1 }{ x }\] Each fraction represents the amount of the lawn mowed in one hour. The fraction of \[\frac{ 1 }{ 2 }\] is John’s portion. Maria’s share is represented by \[\frac{ 1 }{ 4 }\]. The time it would take for both of them to mow the lawn is represented by \[\frac{ 1 }{ x }\]. Solve the rational equation. Show your work.
anonymous
  • anonymous
@Hero
anonymous
  • anonymous
@Aureyliant

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More answers

Hero
  • Hero
Hint: \[x = \dfrac{4 \times 2}{4 + 2}\]
anonymous
  • anonymous
ok Which part is that a hint for? the 1st part?
anonymous
  • anonymous
Do you think you could help me with making a rational equation that goes with a scenario
anonymous
  • anonymous
So if we say that is takes John 2 hours to paint a room and it takes Mary 3 hours to paint the same room. How long would it take for them to paint the whole room together? So would the expression be \[\frac{ 1 }{ 2 } + \frac{ 1 }{ 3 } = \frac{ 1 }{ x }\] ? @Hero
anonymous
  • anonymous
You're already in great hands getting help from Hero :)
anonymous
  • anonymous
Ok
anonymous
  • anonymous
I was just wondering because I need help solving it
anonymous
  • anonymous
So would I get the LCD and solve?
anonymous
  • anonymous
|dw:1434661772234:dw|
anonymous
  • anonymous
|dw:1434661862797:dw|
anonymous
  • anonymous
@mathstudent55
anonymous
  • anonymous
@mathmate
anonymous
  • anonymous
Is this right?
Hero
  • Hero
When solving a rational equation, and you need to add fractions you only need to create an LCD for the two fractions you are adding together.
Hero
  • Hero
Furthermore, including more x's in your equation is probably not a good idea.
anonymous
  • anonymous
Ok so would it be |dw:1434662193097:dw|
Hero
  • Hero
The original equation you set up only had one x to begin with. You want to try to keep it that way.
Hero
  • Hero
That's much better.
anonymous
  • anonymous
Ok then what do I do?
anonymous
  • anonymous
Multiply by 1 to isolate x?
Hero
  • Hero
Also, here's an idea to remember about solving these. Whatever x is, it should always be less than the least time it takes one person to complete a job.
anonymous
  • anonymous
Ok
Hero
  • Hero
Basically, to finish, you solve for x.
Hero
  • Hero
Isolate x.
anonymous
  • anonymous
So I would do \[\frac{ 5 }{ 6 } \times 1 = \frac{ 1 }{ x } \times 1 ?\]
Hero
  • Hero
Ever heard of cross multiplication?
anonymous
  • anonymous
Yes
Hero
  • Hero
Any time you set two fractions equal to each other, you can cross multiply as a strategy for solving for an unknown variable.
anonymous
  • anonymous
so would it be |dw:1434662530398:dw|
anonymous
  • anonymous
?
Hero
  • Hero
\(\dfrac{5}{6} \times \dfrac{1}{x}\) is not the same as \(\dfrac{5}{6} = \dfrac{1}{x}\)
Hero
  • Hero
Try to avoid confusing yourself. \(\dfrac{5}{6} = \dfrac{1}{x}\) becomes \(5x = 6\) after cross multiplication.
anonymous
  • anonymous
Ok so then I would isolate x by dividing both sides by 5?
Hero
  • Hero
Yes. And you would end up with \(x = \dfrac{6}{5}\) but more importantly, what you want to do is convert \(\dfrac{6}{5}\) to a mixed fraction, you'll have \(x = 1 + \dfrac{1}{5}\) which is less than 2 (the time it takes John to complete the job) so the answer makes sense. If both John and Mary work together to complete the job, it should take less time than it would take either of them to complete the job working alone.
anonymous
  • anonymous
Ok thank you so much for your help I feel like I really understood after you helped me I appreciate it a lot. Thanks so much!
Hero
  • Hero
yw

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