Question

A piece of land is shaped like a right triangle. Two people start at the right angle of the
triangle at the same time, and walk at the same speed along different legs of the triangle.
If the area formed by the positions of the two people and their starting point (the right
angle) is changing at 2 m2/s, then how fast are the people moving when they are 3 m
from the right angle? (Round your answer to two decimal places.)

Answer 1

related rates - calculus problem

Answer 2

lets call A area
person one x
person two y
so for any time :
A = x*y/2

now
dA/dt = (dx/dt) * y / 2 + x * (dy/dt) / 2

can you do it now ?

Answer 3

it was better to write :

dA/dt = (dA/dx) * (dx/dt) + (dA/dy) * (dy/dt) = (dx/dt) * y / 2 + x * (dy/dt) / 2

Answer 4

thanks, sorry my internet was not working

Answer 5

maybe my numbers are incorrect

Answer 6

both distances are 3 correct? ie x and y

Answer 7

dx/dt and dy/dt are both 2 correct

Answer 8

no, dA/dt = 2
you want to find dx/dt which is the same as dy/dt

Answer 9

oh, let me work that out

Answer 10

thank you :)

Answer 11

yw