jmc

Question

As Emily is riding her bicycle on a long straight road, she spots Emerson skating in the same direction 1/2 mile in front of her. After she passes him, she can see him in her rear mirror until he is 1/2 mile behind her. Emily rides at a constant rate of 12 miles per hour, and Emerson skates at a constant rate of 8 miles per hour. For how many minutes can Emily see Emerson?

Accepted Answer

Because they are both moving in the same direction, Emily is riding relative to Emerson 12-8=4 mph. Now we can look at it as if Emerson is not moving at all [on his skateboard] and Emily is riding at 4 mph. It takes her 12 mile 1 hour4 miles = 18 hour to ride the 1/2 mile to reach him, and then the same amount of time to be 1/2 mile ahead of him. This totals to 2 18 hour 60 minutes1 hour = 15 minutes