anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
jim_thompson5910
  • jim_thompson5910
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?
anonymous
  • anonymous
No im so sorry this isn't my strongest subject.
jim_thompson5910
  • jim_thompson5910
what is the LCD of all the fractions?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Wouldn't it be 1?
jim_thompson5910
  • jim_thompson5910
|dw:1436836674900:dw|
jim_thompson5910
  • jim_thompson5910
it's actually 4y(y+15) |dw:1436836700642:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1436836726938:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1436836739541:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1436836751079:dw|
anonymous
  • anonymous
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:)
anonymous
  • anonymous
Thank you guys for the help!!
jim_thompson5910
  • jim_thompson5910
so you see how the LCD is 4y(y+15) ?
anonymous
  • anonymous
Brian's time to build the car on his own is 20 hours
anonymous
  • anonymous
Yeah I see it now. Thank you!!
anonymous
  • anonymous
your welcome......
jim_thompson5910
  • jim_thompson5910
ok tell me what you get for y
anonymous
  • anonymous
Wait you would distribute it right?
jim_thompson5910
  • jim_thompson5910
did you multiply all the fractions by the LCD?
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
Okay Thank you!!
jim_thompson5910
  • jim_thompson5910
you're welcome

Looking for something else?

Not the answer you are looking for? Search for more explanations.