Amusement Ride Mathematics

The Sky Trail is a gondola ride through the redwood forests in Del Norte County, near Redwood National and State parks. As we waited in line to board, we were pondering Amusement Ride Mathematics.

A few facts for consideration:

  • Passengers are picked up every 2 minutes
  • Each passenger pays, on average, $10 for the ride
  • Four people, on average, fit in a car
  • The ride to the top of the mountain takes 10 minutes

Riding the Sky Trail.

Passengers loading the Sky Trail.

Solve some Amusement Ride Mathematics

Amusement Ride Mathematics
Click to download printable worksheet

Amusement Ride Mathematics – data table

How long until the person in the red shirt gets on the ride?


Economics: If the sky trail costs $125,000 per year to operate, how many passengers must it have per year to make sure it does not go out of business? (meaning make a profit- could discuss what that means.)

Customer service: Have you been in the line at the grocery store?  Studies show that customers are upset and may even leave if they must wait more than 20 minutes in a line like the Sky trail.  What is the longest line (number of people)  the sky trail managers should allow if customers will be upset if they wait more than 20 minutes? (Could discuss waiting times and what that means.)

Arrival and departure rates:  If customers depart on the sky trail at 4 every two minutes, how many people can ride in an hour?  What is the maximum number of people who can arrive at the ride every 8 minutes if we want to be sure the line does not get too long?