This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.Tutorial ExerciseA boat leaves a dock at 4:00 PM and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 5:00 PM How many minutes after 4:00 PM were the two boats closest together?Part 1 of 7Let t be the time, in hours, after 4:00 PM If the position of the boat at t = 0 corresponds to the origin, then the position of the boat heading south at time t is(x, y) =  $$0 , $$−20t .Part 2 of 7The position of the boat heading east at time t is(x, y) = (15 -15 + 15t, 0 0 ).Part 3 of 7The distance D between the two boats is given byD = 15 225 (t − 1)2 + (-20) 400 t2.Part 4 of 7We will minimizef(t)  =  [D(t)]2 =  225(t − 1)2 + 400t2 =  625 625 t2 − 450 450 t + 225 225 .Part 5 of 7We have f '(t) = t − .

A boat takes 2 hours to move downstream and 3 hours to move upstream between two fixed points in a river. What is time taken by boat to cover one side journey in still water

At noon, ship A is 150 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 20 km/h. How fast (in km/hr) is the distance between the ships changing at 4:00 p.m.? (Round your answer to three decimal places.)

A boat with a speed of 21 km/hr in still water, travels frompoint A to B in the downstream direction and returns topoint A. Another boat with speed of 28 km/hr travels from Bto A and returns to point B. The difference between the timetaken by them to cover the distance is 6.5 hrs. What is thedistance between points A and B, if the speed of stream is 7km/hr?(a) 420 km(b) 120 km(c) 280 km

A man (M) is standing on the bank of a river that is 0.8 miles0.8 miles wide. He wants to reach a house (B) on the opposite shore that is 1.4 miles1.4 miles downstream. The man can row the boat 3mph3⁢mph and can walk 4.5mph4.5⁢mph. Find the distance between the house and the point (P) where he should dock his boat in order to minimize the total time he would need to reach the house. Enter the exact answer or round to the nearest hundredth.

The speed of a boat in still water is 6 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 22.5 km and comes back to the starting point. The total time taken by him is?Options10 hours4 hours 10 minutes6 hours 10 minutes8 hours