Question

Can someone check my work please? Will 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

What do you think it is?

Answer 2

I set it up as 1/(x + 15) + 1/x = 1/4
Then I made the common denominator 4x(x + 15), and got 4 + 4(x+15) = x(x+15)

Answer 3

The 4 + 4(x + 15) = x(x + 15) was the numerators

Answer 4

sorry, if I call t_J time necessary to John to build the model car, then I got this equation fot t_J:
\[t _{J}^{2}+7t _{J}-60=0\]
from which
\[t _{J}=5 hours,\]
and
t_B=time necessary to Brian to build the model car
\[t _{B}=t _{J}+15=5+15=20hours\]
is it right?

Answer 5

@kobeni-chan

Answer 6

oh I didn't think of it like that. In my class they were telling us to set them up as fractions, hold on a minute

Answer 7

@kobeni-chan your equation is right!

Answer 8

@kobeni-chan please, note that, it is the same that I used to find the above values!

Answer 9

ohh ok

Answer 10

in which your x, is my t_J

Answer 11

oh ok. Is It possible for you to figure out what x is through my way w/ the numerators? (sorry if that sounds bossy but I need to explain each step and that's the farthest I got)

Answer 12

ok! I will give you the entire explanation! @kobeni-chan

Answer 13

Solve the following for b and j:\[b-15=j,\frac{1}{b}+\frac{1}{j}=\frac{1}{4} \]\[b=20,j=5 \]

Answer 14

I call W the wor and Brian have to do in order to build the car.
Furthrtmore I call x the time that Jonn used to build the car, and y the time that Brian used to build the same car.
Now from text of your problem we can write:
y=x+15,
do you agree? @kobeni-chan

Answer 15

ok yes

Answer 16

sorry ....I call with W the work that John and Brian have to do....

Answer 17

now rate r_J of John is:
\[r _{J}=\frac{ W }{ x }\]
and rate r_B of Brian is:
\[r _{B}=\frac{ W }{ y }\]
furthermore, from text of your problem, we can write:
\[\frac{ W }{ x+y }=4\]
do you agree?

Answer 18

Ok that makes sense, but my teacher wants me to use only x :/

Answer 19

ok! please note that:
\[r _{B}=\frac{ W }{ x+15 }\]
do you agree?

Answer 20

Yes

Answer 21

now, we can write, from text of your problem:
\[r _{B}+r _{J}=\frac{ W }{ x+15 }+\frac{ W }{ x }=\frac{ W }{ 4 }\]
do you agree?

Answer 22

@kobeni-chan

Answer 23

Ok yes

Answer 24

perfect! please divide by W, both sides of the above equation, and you will get your equation

Answer 25

I thought there wasn't a value for W? :/ sorry I feel confused

Answer 26

@Michele_Laino thanks for taking the time to explain all that to me :)

Answer 27

@kobeni-chan thank you!