Ben starts walking along a path at 3 3 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 6 6 mi/h. How long will it be before Amanda catches up to Ben?

3 hours

Explanation:

Given:

- The speed of Ben v_b = 3 mi/h

- The speed of Amanda v_a = 6 mi/h

- The total time taken to cover distance(d) by ben = t_b

Find:

How long will it be before Amanda catches up to Ben?

Solution:

- The distance d traveled by Ben:

                                 d = v_b*t_b

                                 d = 3*t_b

- The distance d traveled by Amanda:

                                 d = v_a*t_a

                                 d = 6*t_a

- Equate the distance as when they meet:

                                 3*t_b = 6*t_a

- Where ,

                                  t_b = t_a + 1.5

                                  t_a = t_b - 1.5

- Substitute the time relationship in distance relationship:

                                  3*t_b = 6*(t_b - 1.5)

                                  3*t_b = 6*1.5

                                      t_b = 2*1.5 = 3 h

- Hence, It would take 3 hours since Ben starts walking that amanda catches up.