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anonymous

  • one year ago

I will give a medal who answers this and fan them It takes Brian 15 hours longer to build a model car than it takes John. If they work together, they can build the model car in 4 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Brian to build the car on his own

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  1. jim_thompson5910
    • one year ago
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    x = time it takes for Brian to build the model car on his own y = time it takes for John to build the model car on his own we're told that `It takes Brian 15 hours longer to build a model car than it takes John` so x = y+15 \[\large \frac{1}{\text{Brian's Time}}+\frac{1}{\text{John's Time}} = \frac{1}{\text{Time if they work together}}\] \[\large \frac{1}{x}+\frac{1}{y} = \frac{1}{4}\] \[\large \frac{1}{y+15}+\frac{1}{y} = \frac{1}{4}\] Do you know how to solve for y from here?

  2. anonymous
    • one year ago
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    No im so sorry this isn't my strongest subject.

  3. jim_thompson5910
    • one year ago
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    what is the LCD of all the fractions?

  4. anonymous
    • one year ago
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    Wouldn't it be 1?

  5. jim_thompson5910
    • one year ago
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    |dw:1436836674900:dw|

  6. jim_thompson5910
    • one year ago
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    it's actually 4y(y+15) |dw:1436836700642:dw|

  7. jim_thompson5910
    • one year ago
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    |dw:1436836726938:dw|

  8. jim_thompson5910
    • one year ago
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    |dw:1436836739541:dw|

  9. jim_thompson5910
    • one year ago
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    |dw:1436836751079:dw|

  10. anonymous
    • one year ago
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    First, we want to determine the rate at which both John and Brian work. Since we don't know how long it takes John to build the car, we will let x denote this time. If it takes John x hours to build the car, then we know that it takes Brian (x+15) hours to build the car because that's what the problem states. If we can set up an equation that determines x, then all we need to do is add 15 hours to it and we have Brian's time. Now, we can determine the rate at which each boy works. We can clearly see that John works at the rate of 1/x of the model car per hour and Brian works at the rate of 1/(x+15) of the model car per hour. We are told that if they work together, they can build the model car in 4 hours which means that, together, they work at the rate of 1/4 of the model car per hour. We also know that, together, they work at the rate of 1/x + 1/(x+15) of the model car per hour. Thus, our equation to solve is: 1/x + 1/(x+15)=1/4 When we solve this equation for x and add 15 hours to it, we will have solved the problem:)

  11. anonymous
    • one year ago
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    Thank you guys for the help!!

  12. jim_thompson5910
    • one year ago
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    so you see how the LCD is 4y(y+15) ?

  13. anonymous
    • one year ago
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    Brian's time to build the car on his own is 20 hours

  14. anonymous
    • one year ago
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    Yeah I see it now. Thank you!!

  15. anonymous
    • one year ago
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    your welcome......

  16. jim_thompson5910
    • one year ago
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    ok tell me what you get for y

  17. anonymous
    • one year ago
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    Wait you would distribute it right?

  18. jim_thompson5910
    • one year ago
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    did you multiply all the fractions by the LCD?

  19. jim_thompson5910
    • one year ago
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    Multiply every fraction by the LCD 4y(y+15) to get this \[\large \frac{1}{y+15}+\frac{1}{y} = \frac{1}{4}\] \[\large {\color{red}{4y(y+15)*}}\frac{1}{y+15}+{\color{red}{4y(y+15)*}}\frac{1}{y} = {\color{red}{4y(y+15)*}}\frac{1}{4}\] \[\large 4y{\color{red}{{(y+15)}}}*\frac{1}{{\color{red}{{y+15}}}}+4{\color{red}{{y}}}(y+15)*\frac{1}{{\color{red}{{y}}}} = {\color{red}{{4}}}y(y+15)*\frac{1}{{\color{red}{{4}}}}\] \[\large 4y{\color{red}{\cancel{(y+15)}}}*\frac{1}{{\color{red}{\cancel{y+15}}}}+4{\color{red}{\cancel{y}}}(y+15)*\frac{1}{{\color{red}{\cancel{y}}}} = {\color{red}{\cancel{4}}}y(y+15)*\frac{1}{{\color{red}{\cancel{4}}}}\] \[\large 4y + 4(y+15) = y(y+15)\] notice how the denominators canceled out. From here, solve 4y + 4(y+15) = y(y+15) for y

  20. anonymous
    • one year ago
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    Okay Thank you!!

  21. jim_thompson5910
    • one year ago
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    you're welcome

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