Question

Two aeroplanes fly eastwards on parallel courses 12 miles apart. One flies at 240 m.p.h. and the other at 300 m.p.h. How fast is the distance between them changing when the slower plane is 5 miles farther east than the faster plane?

Answer 1

I'll assume you meant that the faster plane is 5 miles farther east...

say the slow one is flying along the x-axis, and the faster one along the line y=12. Then at time t hours, the distance z between them is

z^2 = (300t - 240t)^2 + 12^2
= 3600t^2 + 144
300t-240t = 5 when t=1/12
at that time, z=13

2z dz/dt = 7200t
dz/dt = 20 mi/hr