Question

A car traveling north at 40 mph and a truck traveling east at 30 mph leave an intersection at the same time. At what rate will the distance between them be changing 3 hours later? (Let D(t) denote the distance between them at time t .)

Answer 1

so do i differentiate pythagorean theorem?

Answer 2

\[D^2=x^2+y^2\]
\[2DD'=2xx'+2yy'\]
\[x'=40, y'=30\]

Answer 3

ok makes sense so far

Answer 4

yeah differentiate using pythagoras
now one one hour later x and y are 30 and 40 respectively, so you know by pythagoras that D =50
plug in the numbers, solve for D'

Answer 5

oh that was a mistake, 3 hours later

Answer 6

so x and y are 90 and 120

Answer 7

3 hours later x is 120, and y is 90 so by pythagoras D is 150

Answer 8

how did you get 150

Answer 9

would it not be 210

Answer 10

hmm maybe

Answer 11

or sort of 210

Answer 12

you have a 3 - 4 - 5 right triangle

Answer 13

i meant sqrt 210

Answer 14

3- 4- 5
30 -40 -50
90- 120 - 150

Answer 15

it is 150

Answer 16

whoa that just blew my mind what is that all about?

Answer 17

ok i see you just multiplied all by 30 right

Answer 18

\[\sqrt{90^2+120^2}=\sqrt{22500}\]

Answer 19

right exactly just used the ratios, but you get 150 in any case i am sure

Answer 20

so 150 is the answer thats my rate at which the distance is changing

Answer 21

oh no , that is D

Answer 22

you have
\[2CC'=2xx'+2yy'\]

Answer 23

right

Answer 24

\[2D'D=2xx'+2yy'\]

Answer 25

or better yet
\[DD'=xx'+yy'\]

Answer 26

you know
\[x'=40,x=120, y'=30,y=90, D=150\] and you want D'

Answer 27

plug in the numbers, solve for D'

Answer 28

\[150D'=120\times 40+90\times 30\] etc

Answer 29

ok, i guess i understand it now for this problem but the real problem I'm having is finding what my variables to assign in each problem

Answer 30

you get to pick the variable. trick is to find the equation relating them

Answer 31

and i just worked that out and got 50 and that is not correct

Answer 32

look for similar triangles, pythagoras etc
ok lets see

Answer 33

\[150D'=40\times 120+30\times 90\]
yeah i get 50 as well

Answer 34

why is 50 mph wrong? it looks good to me

Answer 35

beats me man... this stuff is mind boggling to me. I've actually posted like 3 or 4 questions up here from my homework this week and no one has yet been able to help me...

Answer 36

how do you know it is wrong?

Answer 37

i am fairly sure it is right

Answer 38

ok nevermind man it was asking for it in kilometers i don't know why... so i converted it and it was correct

Answer 39

lord just to confuse you
ok fine, now we got it right?