Question

At noon three students, Abby, Ben, and Cassie, are standing so that Abby is m west of Ben and Cassie is m east of Ben. While Ben stays in his initial position, Abby begins walking south at a constant rate of m/min and Cassie begins walking north at a constant rate of m/min. In how many minutes will the distance between Cassie and Ben be twice the distance between Abby and Ben?

Answer 1

Let represent the number of minutes until Cassie’s distance to Ben is twice that of Abby’s distance to Ben. In minutes Abby will walk m and Cassie will walk m. The following diagram contains the information showing Abby’s position, , Ben’s position, , and Cassie’s position, , at time .

A right-angled triangle is formed by joining Abby's initial position to points A and B. Its hypotenuse is A B and its other sides are of length 100 and 20 times t. Another right-angled triangle is formed by joining Cassie's initial position to points C and B. Its hypotenuse is B C and its other sides are of length 160 and 41 time. Represent Abby, Ben and Cassie’s respective positions at noon as points on the -axis so that Ben is positioned at the origin , Abby is positioned units left of Ben at and Cassie is positioned units right of Ben at .

solution 2

Let represent the number of minutes until Cassie’s distance to Ben is twice that of Abby’s distance to Ben.

In minutes Abby will walk south m to the point . In minutes Cassie will walk north m to the pointTherefore, in

minutes ( minutes seconds), Cassie’s distance to Ben will be twice that of Abby’s distance to Ben. .