Answer the following with complete solutions and illustration

Maxima & Minima 1. A trapezoidal gutter is to be made, from a strip of metal 24 inches wide by bending up the edges. If the base is 16 inches wide, what width across the top gives the greatest carrying capacity. 2. A wall 8 ft high is 6 ft from the house. Find the length of the shortest ladder that will reach the house, when one end rests on the ground outside the wall. 3. A wall 12 ft high is 6 ft from the house. Find the length of the shortest ladder that will reach the house, when one end rests on the ground outside the wall. 4. A man in a motorboat at A receives a message at noon, calling him to B. A bus making 50 miles per hour leaves C, bound for B, at 1:00 PM. If AC = 40 miles, what must be the speed of the boat, to enable the man to catch the bus? 5. A pole 22 feet long is carried horizontally along a corridor 6 feet wide and into a second corridor at right angles to the first. How wide must the second corridor be?