A boat leaves a dock at 2:00 PM and travels due south at a speed of 30 km/h. Another boat has been heading due east at 25 km/h and reaches the same dock at 4:00 PM. At what time were the two boats closest together?
When the southbound boat left the dock, the other boat was 50 km from the dock.
let the distance between them be d
d^2 = (30t)^2 + (50-25t)^2
2d dd/dt = 2(30t)(30) + 2(50-25t)(-25)
d dd/dt = (30t)(30) + (50-25t)(-25)
d dd/dt = 900t - 1250 + 625t
dd/dt = 0 at a min of d.
1525t = 1250
t = 1250/1525 hours
= 50/61 hours or appr 49 minutes after the southbound boat left the dock.
check my calculations.