What integer represents the distance the snail traveled from its original position?

Question

A snail climbs 3 inches then slides 6 inches. What integer represents the distance the snail traveled from its original position?

Answer 1

Hi Alicia - I think that your word problem may suffer from poor wording.

 

    DISTANCE deals with the actual path taken - direction does not matter. For example, if you drive your car 3 miles north, then 6 miles east, you have driven a total DISTANCE of 9 miles.  By the wording of the problem given, the answer should be 9 inches.

 

    However, if we are concerned with calculating DISPLACEMENT, we are only concerned with the overall change in position from start to finish.

 

  In this case, we want to construct a triangle showing the path taken, and calculate the distance between the start and end points.

 

  _ _ _6_ _ _

  |

3|

  |

 

 

    For a right triangle, we can calculate the "displacement" (hypotenuse) using the Pythagorean Theorem: a² + b² = c²

 

    So the overall displacement (hypotenuse) = √(3²+6²)

 

    Displacement = √(45)

 

                        = √(9) * √(5)

 

                        = 3 √(5)