Week #7 Winter 2015
of the Week
Solution
On Stuppenga Road there is a traffic light every mile. Each light is synchronized
to turn green, yellow and red at the same times. Green lights last 40 seconds,
yellow lights last 5 seconds and red lights last 35 seconds. The speed limit on
Stuppenga Road is 60 miles per hour. What is the maximum speed (assuming
you adhere to the speed limit) that you could go so that you hit every light while
it is green (assume that you have no issues with traffic)?
Solution: If you attempt to drive 60 miles per hour, you will get to an intersection every 60
seconds. If you hit the first green light at n seconds into the green light, you will have to hit the
next green light at 20+n seconds into the green light and the third green light at 40+n seconds
into the green light, but green lights only last 40 seconds and n can be at most 40. This makes it
impossible to hit all green lights at 60 miles per hour. If you instead travel 45 miles per hour you
will pass an intersection every 80 seconds. Because of this, if you get one green light, they will
all be green. The fastest you can travel is 45 miles per hour.