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anonymous

  • one year ago

I need help someone. Can someone please help me?

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  1. anonymous
    • one year ago
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    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.

  2. anonymous
    • one year ago
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    @Hero

  3. anonymous
    • one year ago
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    @Aureyliant

  4. Hero
    • one year ago
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    Hint: \[x = \dfrac{4 \times 2}{4 + 2}\]

  5. anonymous
    • one year ago
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    ok Which part is that a hint for? the 1st part?

  6. anonymous
    • one year ago
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    Do you think you could help me with making a rational equation that goes with a scenario

  7. anonymous
    • one year ago
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    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

  8. anonymous
    • one year ago
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    You're already in great hands getting help from Hero :)

  9. anonymous
    • one year ago
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    Ok

  10. anonymous
    • one year ago
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    I was just wondering because I need help solving it

  11. anonymous
    • one year ago
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    So would I get the LCD and solve?

  12. anonymous
    • one year ago
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    |dw:1434661772234:dw|

  13. anonymous
    • one year ago
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    |dw:1434661862797:dw|

  14. anonymous
    • one year ago
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    @mathstudent55

  15. anonymous
    • one year ago
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    @mathmate

  16. anonymous
    • one year ago
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    Is this right?

  17. Hero
    • one year ago
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    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.

  18. Hero
    • one year ago
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    Furthermore, including more x's in your equation is probably not a good idea.

  19. anonymous
    • one year ago
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    Ok so would it be |dw:1434662193097:dw|

  20. Hero
    • one year ago
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    The original equation you set up only had one x to begin with. You want to try to keep it that way.

  21. Hero
    • one year ago
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    That's much better.

  22. anonymous
    • one year ago
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    Ok then what do I do?

  23. anonymous
    • one year ago
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    Multiply by 1 to isolate x?

  24. Hero
    • one year ago
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    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.

  25. anonymous
    • one year ago
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    Ok

  26. Hero
    • one year ago
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    Basically, to finish, you solve for x.

  27. Hero
    • one year ago
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    Isolate x.

  28. anonymous
    • one year ago
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    So I would do \[\frac{ 5 }{ 6 } \times 1 = \frac{ 1 }{ x } \times 1 ?\]

  29. Hero
    • one year ago
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    Ever heard of cross multiplication?

  30. anonymous
    • one year ago
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    Yes

  31. Hero
    • one year ago
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    Any time you set two fractions equal to each other, you can cross multiply as a strategy for solving for an unknown variable.

  32. anonymous
    • one year ago
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    so would it be |dw:1434662530398:dw|

  33. anonymous
    • one year ago
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    ?

  34. Hero
    • one year ago
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    \(\dfrac{5}{6} \times \dfrac{1}{x}\) is not the same as \(\dfrac{5}{6} = \dfrac{1}{x}\)

  35. Hero
    • one year ago
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    Try to avoid confusing yourself. \(\dfrac{5}{6} = \dfrac{1}{x}\) becomes \(5x = 6\) after cross multiplication.

  36. anonymous
    • one year ago
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    Ok so then I would isolate x by dividing both sides by 5?

  37. Hero
    • one year ago
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    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.

  38. anonymous
    • one year ago
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    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!

  39. Hero
    • one year ago
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    yw

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