## 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

1. 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?

2. anonymous

No im so sorry this isn't my strongest subject.

3. jim_thompson5910

what is the LCD of all the fractions?

4. anonymous

Wouldn't it be 1?

5. jim_thompson5910

|dw:1436836674900:dw|

6. jim_thompson5910

it's actually 4y(y+15) |dw:1436836700642:dw|

7. jim_thompson5910

|dw:1436836726938:dw|

8. jim_thompson5910

|dw:1436836739541:dw|

9. jim_thompson5910

|dw:1436836751079:dw|

10. 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:)

11. anonymous

Thank you guys for the help!!

12. jim_thompson5910

so you see how the LCD is 4y(y+15) ?

13. anonymous

Brian's time to build the car on his own is 20 hours

14. anonymous

Yeah I see it now. Thank you!!

15. anonymous

16. jim_thompson5910

ok tell me what you get for y

17. anonymous

Wait you would distribute it right?

18. jim_thompson5910

did you multiply all the fractions by the LCD?

19. 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

20. anonymous

Okay Thank you!!

21. jim_thompson5910

you're welcome