Question

ILL FAN & GIVE YOU MEDAL!!!!!!!






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. explain each step in figuring out how to determine the time it would take Brian to build the car on his own.

Answer 1

sure

Answer 2

and here comes mathbreaker :/

Answer 3

if it takes john x hours, it takes brian x + 15.
hence john does 1/x of the work every hour, but brian takes 1/(x+15)
Oh sorry saber, ill give you this one haha ;)

Answer 4

:/

Answer 5

You want to take this? :| or should i :P

Answer 6

go on

Answer 7

u kinda confused me with ure answer are u sure its right?

Answer 8

He's correct so far @xrosaber

Answer 9

idk im not tht good in maths

Answer 10

when it comes to word problems i suk

Answer 11

so i set up the equation 1/x + 1/x+5 = 1/4?

Answer 12

Yes thats right bubbles :)

Answer 13

Solve for x, and just add 15 to get brians time :)

Answer 14

Right...because

John = 1 car in 'x' hours
Brian = 1 car in 'x + 15' hours...

so together ...if it takes 4 hours we have

\[\large \frac{1}{x} + \frac{1}{x + 15} = \frac{1}{4}\]

Answer 15

makes more sense i neeed to improve in word problems :(

Answer 16

oh i thought you would put 1/15x to get brains time o: & Next i find the LCM correct?

Answer 17

yes and youll get 8x + 60 = x^2 + 15x
x^2 + 7x + 60 = 0...
remember that when you take quadratic, take the positive answer always cause time cannot be negative

Answer 18

Check you equation again @Mathbreaker

Answer 19

i thought the LCM would be 4x(x+5)......

Answer 20

\[\large 8x + 60 = x^2 + 15x\]
becomes
\[\large x^2 + 7x - 60 = 0\]

Answer 21

im so confused

Answer 22

@bubbles-are-cool. That is the LCM :)

4x(x + 15)

remember it is 15 not 5 :)

Answer 23

Haha sorry i did that mentally so i missed that :P
Im sorry, its x^2 + 7x -60 = 0

Answer 24

So we have

\[\large \frac{1}{x} + \frac{1}{x + 15} = \frac{1}{4}\]

Find the LCM (Least common denominator) which as @bubbles-are-cool. has said it is 4x(x + 15)

What do we do next?

Answer 25

guyz wht grade math is this

Answer 26

Algebra 2 x: & next youd get the common denominator ?

Answer 27

This would be grade 7-9 math :)

Answer 28

-.-

Answer 29

honestly

Answer 30

im in grade 10 havent even been close to studying stuff like that

Answer 31

im in 10th too

Answer 32

which school

Answer 33

flvs

Answer 34

oh

Answer 35

Wow... im in grade 10
you should come to india we have already started differentiation and integration. india studies are fun. but they're only for people who like it :P

Answer 36

i guess we have different curricualm

Answer 37

im horrible at math x.x

Answer 38

Right...since that is 4x(x + 15)....multiply that to the 2 fractions you have on the left...and dont forget to multiply it to the other side too...

\[\large \frac{4x(x + 15)}{x} + \frac{4x(x + 15)}{x + 15} = \frac{4x(x + 15)}{4}\]
becomes
\[\large 4(x + 15) + 4x = x(x + 15)\]

Now what?

Answer 39

Haha youre not. its all about practice :)

Answer 40

Wow john youre working hard :)
Is that a question aimed at us or bubbles?:P

Answer 41

Right everyone learns at a different pace and sometimes it takes more than 1 way of looking at a problem to get it :)

Answer 42

Lol ehh in general ...everyone! lol :D

Answer 43

now you distribute to simplify ? :o

Answer 44

oh. then you equate the sides to get a quadratic equation, use the discriminant formula, get the x, take the positive value, and add 15 to it :P
and there you have it, the asnwer :P

Answer 45

Mmhmm...distribute everything you can...what do you get @bubbles-are-cool.

Answer 46

4x+60+4x = x^2 +15x
and if when you add the 4x you get : 8x+60 = x^2 +15x

Answer 47

Right...so now you have that

\[\large 8x + 60 = x^2 + 15x\]

Now any terms you can combine?

Answer 48

8x and 15x?

Answer 49

Mmhmm you can subtract 8x from both sides...

\[\large x^2 + 7x = 60\]

You can see this is turning into a quadratic...so go ahead and subtract 60 from both sides too

\[\large x^2 + 7x - 60 = 0\]

Answer 50

Now you just use the quadratic equation to solve for your 'x' :)

Answer 51

How would i do that if i have an exponent?

Answer 52

Well remember the quadratic equation uses the coefficients of this equation..

in the form

\[\large ax^2 + bx + c = 0\]

The coefficients are 'a' 'b' and 'c' right?

So here...

\[\large x^2 + 7x - 60\]

a = 1
b = 7
c = -60

Make sense?

Answer 53

yes c:

Answer 54

Perfect :)

So you plug them into the quadratic equation...just in case you need to see it again...

\[\large \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Answer 55

yes & now i have
-7 +- (sq289) / 2

Answer 56

do i find the squareroot?

Answer 57

Yes you do :)

Answer 58

now i have -7 +- 17 / 2
would i add or subtract next?

Answer 59

Well now...you have 2 equations...

\[\large \frac{-7 + -17}{2}\]
and
\[\large \frac{-7 - (-17)}{2}\]

Solve both, what do you get?

Answer 60

the first answer is -12 and the second is 5

Answer 61

Perfect...

Now we know...time isn't negative....so we can discard that -12 okay?

So our x that we solved is 5....(not the answer yet) but ready for the last step?

Answer 62

yes next i add 15?

Answer 63

Haha perfect beat me to it :)

Answer 64

so the answer is 20 c:

Answer 65

That is correct :)

Answer 66

thanks !

Answer 67

Anytime :) Great Work @bubbles-are-cool.