Lisa started on a two mile circular hike. After hiking 0.5 mile she took a short cut and rejoined the circular path. How far did she walk when she returned?

Question

round to the nearest tenth of a mile

Answer 1

 

So think of the diagram as the coordinate plane.

 

By number, starting with 1 and ending at 7, I have diagrammed Lisa's path.

 

Since it is a 2 mile track, that means when she is on the circular path (Quadrants 1 & 4)

she walks 1/2 mile in each of those 2 quadrants

 

The distance around the track is 2 miles.  That is equivalent to the circumference of the circular track.

We us this info to determine the diameter of the circle.

 

   pi • diameter = 2 miles

         diameter = 2 / pi

         

 

so since she takes a shortcut from point 3 to 4 to 5, that distance represents the diameter

of the circle.

 

So her total distance is

   

      from 1 to 2 to 3 => .5 miles

      from 3 to 4 to 5 => 2/pi miles = .63662 milrs

      from 5 to 6 to 7 => .5 miles

 

Total distance 1.63662 miles = 1.6 miles

 

 

                            3

                            |

                            |                2

                            |                

                            |

                            |

----------------------4---------------------- 1 & 7

                            |

                            |

                            |    

                            |              6

                            |

                            5