Intercampus Firefly

Due to Luc Longpre

Problem: A student is traveling from UTEP towards NMSU by bicycle at 10mph. The student's friend, a NMSU student, is traveling from NMSU towards UTEP at 15mph. The distance between UTEP and NMSU is 45 miles. Meanwhile, a dragonfly starts from the UTEP student's bicycle to the NMSU student's bicycle, then back to the UTEP student, going back and forth until the friends meet. The dragonfly travels at 25mph.

1. What's the distance traveled by the dragonfly?
2. How much of that distance is traveled towards NMSU and how much back towards UTEP?

Extra credit: The problem is spiced up with a wind from NMSU towards UTEP. The wind slows down the UTEP student by 1mph, increases the NMSU student's speed by 1mph, slows down the dragonfly by 5mph in one direction and increases its speed by 5mph in the other direction.

Winners will be selected according to their solution of questions 1 and 2 (with explanations). The extra credit question is just an extra challenge.