I don't know what to do for this max/min word problem. Could someone explain the steps please?

Question

a boat leaves a dock at noon and heads west at a speed of 25km/h. Another boat heads north at 20km/h and reached the same dock at 1:00 pm. When were the boats closest to each other?

Thank you!

Answer 1

at noon, they are 20 km apart, the closest they'll ever be

at 1pm they are 25 km apart

at every point in time after noon, they get further apart

if the northbound boat arrives at the same dock at 1pm after going 20 km/h, then the starting point for the northbound boat is 20 km south of the dock

maybe the problem was intended to ask when the boats were furthest apart? between 1pm and 2pm? and what was that distance.

the distance between them is the hypotenuse of a right triangle with sides 25(t-1) and 20(2-t) if they both left at 1pm

where 1<t<2 and t=1 = 1pm and t=2 means 2pm

the horizontal side = 25t-25

the vertical side = 40--20t

the hypotenuse squared = (25t-25)^2 + (40-20t)^2

h' = (1025t --1425)/h = 0

set the numerator = 0 and solve for time t

between the time the northbound boat starts moving and the time it reaches the dock

the maximum distance between them is at time t = 1425/1025 = 1.39 = 1:39 pm

at 1:39 m the distance between them is about 35.5 km

which is greater than 20 km at 1pm or 25km at 2pm