## A Question Of Time

A student is doing an experiment timing a marble rolling down a 45 degree incline plane (see Figure 1 below). A second student says "I'll bet I can get it to roll to the bottom in less time by using two incline planes like this." (see Figure 2 below). The first student says "Yes your marble will roll faster during the first section, but it also has further to roll. My single plane is the shortest distance between the top and the bottom, therefore my marble will reach the bottom first". Who is right?

• A. The first student is correct. Even thought the second marble rolls faster during it's trip, it has farther to roll so it takes longer than the first.
• B. The second student is correct. The second marble travels at a faster average speed during its journey, and even though the path is somewhat longer, the faster average speed is great enough that the second marble makes the journey in less time that the first marble.
• C. Neither one is correct. Both marbles take the same time to reach the bottom. The faster average speed of the second marble is exactly offset by the longer distance it has to travel.
• D. This is a hard problem. Why don't they just throw the marble down?