D and M were one mile apart when they began walking toward each other

Problem 4

D and M were one mile apart when they began walking toward each other. D walks at a constant rate of 3mph, and M walks at a constant rate of 4 mph. When they started, D’s dog, who ran at a constant rate of 7 mph, ran to M: then turned back and ran to D. If the dog continued to run back and forth until D and M met and lost no time turning around, how far did it run?

[Problem submitted by Iris Magee, LACC Associate Professor of Mathematics.]

Solution for Problem 4:

1 mile. The distance between D and M is decreasing at a rate of 7 mph, therefore it takesof an hour for the distance to decrease from 1 mile to 0. In this time the dog ran mile.