Question

Two buses are driving along parallel freeways that are 5mi apart, one heading east and the other heading west. Assuming that each bus drives a constant 55mph, find the rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other.

Answer 1

I assume highways are east / west and the13 miles is the hypotenuse
13^2 = 5^2 + x^2
55* 2 = 110 =difference in speed east
t in hours
x distance apart = Xi - 110 t
y distance apart = 5
x difference at t = 0 , Xi = sqrt(13^2 - 5^2) = sqrt(169-25) = 12 miles apart east/west at t = 0
s = distance apart = sqrt (x^2 + 5^2) = (x^2+25)^.5
ds/dt = 0.5 (x^2+25)^-.5 * 2 x dx/dt
at t = 0, x = 12 and dx/dt is always 110 mph
ds/dt = 0.5 * 24 *110 mph /(144+25)^.5
= 1320 mph /(13) = 101.53 mph