posted by Rachael .
A helicopter is 400 miles directly north of Ghana and is flying at 20 miles per hour. A second helicopter is 300 miles east of Ghana and is flying west at 15 mph. What is the rate of change of the distance between the helicopters?
You don't say which way the first helicopter is flying, north or south or ...
I will assume it is flying south.
Make a right-angled triangle with y as the remaining distance to Ghana and x as the remaining distance.
let d be the distance between them
d^2 = y^2 + x^2
2d dd/dt = 2ydy/dt + 2xdx/dt
when x=300 and y = 400
d^2 = 300^2 + 400^2
d = 500 (did you recognize the 3,4, 5 triangle ?)
dd/dt = (400(-20) + 300(-15))/(2(500)) = 12.5