Question

I really need help :/ I will fan and give 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. 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.

Answer 1

Hi!

Answer 2

we can do this but it will take a minute or two
ready?

Answer 3

this is where you say "yes, i am ready" or "no forget it"

Answer 4

Yes I am sorry computer glitched

Answer 5

oh ok
i didn't do it in advance but we can work it out i am sure

Answer 6

lets say it takes john \(x\) hours so it takes brian \(x+15\) hours
that means john's rate is \(\frac{1}{x}\) per hour and brians is \(\frac{1}{x+15}\) per hour
now we have to find the combined rate, which we do by adding

Answer 7

the combined rate is
\[\frac{1}{x}+\frac{1}{x+15}=\frac{2x+15}{x(x+15)}\] and it take them 4 hours that rate to do one job, so we have to solve
\[\frac{2x+15}{x(x+15)\times 4=1\]

Answer 8

oops
\[\frac{2x+15}{x(x+15)}\times 4=1\]

Answer 9

let me know where i lost you
solving this equation is not so hard
\[4(2x+15)=x(x+15)\\
8x+60=x^2+15x\] and then you have a quadratic equation to solve

Answer 10

Oh okay I see now. Someone else got the same quadratic equation I just wasn't sure how they got it until now

Answer 11

ok then i guess it is right!

Answer 12

Yes and the number of hours it takes Brian in 20 hours

Answer 13

is*

Answer 14

\[x^2+7x-60=0\\
(x-5)(x+12)=0\\
x=5\]

Answer 15

so john took 5 hours, brian 20

Answer 16

Thank you so much for your help :)

Answer 17

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