Question

Calculus - Related Rates:
From a certain spot X, a car travels due north at a speed of 70 miles per hour. Ten miles east of this spot X, another car travels due south at a speed of 80 miles per hour. How fast is the distance between the two cars increasing the moment they are 40 miles apart?

Answer 1

differentiate \[x^2+y^2=z^2\]

with respect to time t

Answer 2

2x dx/dt + 2y dy/dt =2z dz/dt

Answer 3

good...did you draw a picture...what is x ,y, and z

Answer 4

we can then make a large triangle...

Answer 5

I guess I shouldn't have used X since they are referring to it as a point

Answer 6

i'm with you so far

Answer 7

y=10,z=40...find x

Answer 8

x= \[\sqrt{1500}\]

Answer 9

sorry dude, this script is killing my ie8. had to bail and switch to mozilla.

Answer 10

do you know what x'
and y' are?

Answer 11

yes, x' is 70mph and y' is 80mph

Answer 12

no

Answer 13

y is a fixed 10 miles...so y'=0

Answer 14

ah hah

Answer 15

and x' is not 70

Answer 16

north and south are both vertical displacements so x'=70+80=150

Answer 17

ok, gotcha

Answer 18

plug in all your numbers into your derivative and solve for z'

Answer 19

145.24mph?

Answer 20

yes

Answer 21

awesome, thank you for your help. I was doing some crazy stuff I didn't need to do.

Answer 22

np