**Problem Description:**A lighthouse is located 7 miles off a straight shoreline. Fourteen miles down the coast is a restaurant where the lighthouse keeper is planning to meet his friends. If the keeper can row at a speed of 1.7 mph and walk at 3 mph, the question asks: where should he land on the shoreline, as measured from the point on the shore nearest to the lighthouse, to make the fastest possible time to the restaurant? The answer should be rounded to the nearest whole number.**Illustration:**The accompanying diagram depicts:- A lighthouse positioned in the water.- A perpendicular line from the lighthouse to the shoreline measuring 7 miles.- The shoreline itself leading to a restaurant located 14 miles from the landing point directly below the lighthouse.**Solution Approach:**To solve this problem, consider the following:1. Determine the point on the shoreline where the lighthouse keeper should land to optimize his travel time.2. Use the distances and speeds provided to calculate the minimal time path using calculus or optimization techniques.3. Round the answer to the nearest whole number and report it.**Graphical Representation:**The diagram complements the problem by visually showing the distances involved—the perpendicular distance from the lighthouse to the shore (7 miles) and the horizontal distance along the shore to the restaurant (14 miles).**Answer Section:**Enter the calculated optimal landing distance along the shoreline in the provided box.

According to question,Distance Between lighthouse and shoreline = 7 miFrom The following Figure,Let AB be x mi and PB be l,then, According to pythagoras theorem,l2 = 72 + x2l = 49 + x2Now,Person can Row at the speed of 1.7 mph and walk at the speed of 3 mph,We have assumed that,Person Row 'l' miles and walked '14-x' miles, As Above Figure,so,We know that,Time = Distance Speedso,T = l1.7 + 14-x3T = 49 + x21.7 + 14-x3NowDifferentiate above equation w.r.t 'x'dTdx = 2x1.7×249 + x2 - 13dTdx = x1.749 + x2 - 13For Minimum value of time,dTdx = 0,x1.749 + x2 - 13 = 0x1.749 + x2 = 133x = 1.749 + x23x 1.7=49 + x21.7647 x = 49 + x2squaring both sides,3.11x2 = 49 + x2 2.11 x2 = 49x2 = 492.11x = 4.819 miles AnswerHe Shoul land at 4.819 miles from the point on the shore nearest to the light house.