Question

At 7:00 am, one ship was 60 miles due east from a second ship.If the first ship sailed west at 20 mph, and the second ship sailed southeast at 30 mph, at what time are they closest together?

Answer 1

Assume the ships started at A=(60,0) B=(0,0)

at time x hours,

A is at 60-20x
B is at (21.2x,-21.2x)

the distance d is thus given by

d^2 = (60-20x-21.2x)^2 + (-21.2x)^2

2d dd/dx = 2(60-41.2x)(-41.2) + 2(-21.2x)(-21.3)

we can forget about the denominator and just set the numerator = 0, to get dd/dx = 0 when x = 1.151, = 1:09

So, the ships are closest at 8:09 am

Answer 2

how did you derive where B is at where did the answer 21.2 come from?