Wednesday, June 1, 2011

rate-time-distance problems

Most of the rate-time-distance problems that students find in their Algebra textbooks are contrived and pointless. There's no reason why students should care about how long it would take for two trains separated by 200 miles, one traveling at 45 miles per hour and the other traveling at 65 miles per hour, to pass one another on parallel tracks.

However, current storms and tornado warnings suggest very relevant and much more interesting problems to consider. Meteorologists, or their underpaid underlings, are currently making many similar calculations every minute:

A storm traveling east at 50 miles per hour is currently 32 miles away. How many minutes will it take for the storm to reach your town?

Assuming the storm picks up speed at a rate of 3mph every five minutes, how long will it take to reach your town?

Two storms, one 54 miles to the north and traveling at 52 miles per hour, the other 38 miles to the west and traveling at 45 miles per hour, are headed in your direction. Which will arrive first?

And the list goes on...