# 2. CONDITION

The messenger needs to run 24 miles. Two-thirds of this distance he ran at an average speed of 8 miles per hour. Can he, by increasing his speed, run the remaining distance so that his average speed for the entire journey equals 12 miles per hour?
Solution. To achieve an average speed of 12 miles per hour for the entire journey, the messenger must run 24 miles in 2 hours. But he has already spent these 2 hours on the first 16 miles.

Answer: cannot.