Question

Im horrible at word problems. Calc help plz :/

My aunt and I were approaching the same intersection, she from the south and I from the west. She was traveling at a steady speed of 5 miles/hour, while I was approaching the intersection at 50 miles/hour. At a certain instant in time, I was three-tenths of a mile from the intersection, while she was one-twentieth of a mile from it. How fast were we approaching each other at that instant? (Give your answer to the nearest integer.)

answer should be in MPH

Answer 1

we are going from the west , so we have distance from intersection as i labeled "x" and you are told that
\[x'=50\] (well actually it should be -50 because x is getting smaller)
likewise grandma's distance from intersection is y and you are told
\[y'=5\]

Answer 2

if we call the distance we are from each other "z" then pythagoras tells us that
\[x^2+y^2=z^2\] differentiating gives us
\[2xx'+2yy'=2zz'\]
all the numbers are known except

\[z'\] which is the one we want, so solve for that
\[x'=50,y'=5, x =.3, y = .05, z = \sqrt{.3^2+.05^2}\] plug them in and solve for
\[z'\]