Boats and lillypads

Question

Sam and Kirby were out in their rowboat one day, when Kirby spied a nearby water lily. Knowing that Sam liked a mathematical challenge, Kirby announced that, with the help of the plant, it was possible to calculate the depth of the water under the boat. While Sam held the top of the plant, which remained rooted to the lake bottom during the entire process, Kirby gently rowed the boat five feet. This forced Sam’s hand to the water surface. When pulled taut, the top of the plant was originally 10 inches above the water surface. Use this information to calculate the depth of the water under the boat.

Answer 1

First of all, convert all the numbers in the problem into the same units.....5 ft=60 in.

 

In the boats original position, the length of the plant underwater will be represented by x making the length of the entire plant x+10. As the boat moved 60 inches, the length of the plant becomes the hypotenuse of a right triangle having legs of x and 60. So use the Pythagorean Theorem.

 

x² + 60² = (x+10)²

x²+3600 = x²+20x +100              (x+10)(x+10)

      3600 = 20x + 100

      3500 = 20x

       175 = x

 

So the depth of the water that the water lily is in is 175 inches or 14 feet 7 inches.

 

Hope this helped.