69 - 71 Shortest and most economical path of motorboat

Problem 69
A man on an island 12 miles south of a straight beach wishes to reach a point on shore 20 miles east. If a motorboat, making 20 miles per hour, can be hired at the rate of \$2.00 per hour for the time it is actually used, and the cost of land transportation is \$0.06 per mile, how much must he pay for the trip?

Solution:

 

Problem 70
070-figure-42.jpgA man in a motorboat at A (Figure 42) receives a message at noon calling him to B. A bus making 40 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.

Solution:

 

Problem 71
In Problem 70, if the speed of the boat is 30 miles per hour, what is the greatest distance offshore from which the bus can be caught?

Solution:

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