Difficulty:Hard

Category:Additional Topics in Math / Geometry

Strategic Advice:In this question, information is given in both the diagram and the text. You need to relate the text to the diagram, one piece of information at a time, to calculate how long the lifeguard ran along the beach and how long he swam. Before you find the swim time, you need to know howfarhe swam.

Getting to the Answer:Whenever you see a right triangle symbol in a diagram, you should think Pythagorean theorem or, in this question, special right triangles. All multiples of 3-4-5 triangles are right triangles, so the length of the lifeguard’s swim is the hypotenuse of a 30-40-50 triangle, or 50 feet. Add this number to the diagram. Now calculate the times using the distances and the speeds given. Don’t forget the 1 second that the lifeguard paused.

Run time =$60\overline{)\text{ft}}\times \frac{1\text{ sec}}{12\overline{)\text{ft}}}=\frac{60}{12}=5\text{ sec}$

Pause time = 1 sec

Swim time =$50\overline{)\text{ft}}\times \frac{1\text{ sec}}{5\overline{)\text{ft}}}=\frac{50}{5}=10\text{ sec}$

Total time = 5 + 1 + 10 = 16 seconds