A boat leaves a dock at noon and heads west at a speed of 25 km/hr. Another boat heads north at 20 km/hr and reaches the same dock at 1 p.m. Where were the boats closest?
We can find the minimum distance and thus, the points of Boats A and B.
To do this, we will use a well established formula
Noting that the origin of the XY graph is the dock we can find a location on the x-axis for boat A and a location on the y-axis for boat B.
Boat A is moving west at a rate of 25 km/h for up to an hour. So at 1pm boat A is 25km west of the origin. Thus, the distance increases in the west (the negative direction) with time at a rate of -25t (where t is time).
Boat B is moving north at a rate of 20km/h for up to an hour. So at 12pm the boat is 20km South of the origin. Thus, the distance decreases at a rate of -20 + 20t
From here we can find points to use in our distance formula.
P1( -25t , 0 ) and P2 ( 0 , -20 + 20t )
Note that minimizing will minimize the problem. Thus,
Solve for t and then multiply by the given rates for boat A and boat B to find their distances