To test a new robot, two hundred smooth white stones are placed 3 feet apart in a long straight line on the ground. A basket is placed at the beginning of the line, 3 feet away from the first stone. The robot starts at the basket and collects the stones one by one, putting each stone in the basket before getting the next stone. The robot never moves the basket. It takes awhile. How far does the robot travel? (What is the robot’s name?)
| stone # | distance out and back | ||||
| 1 | 3 + 3 = 6 | ||||
| 2 | 6 + 6 = 12 | ||||
| 3 | 9 + 9 = 18 | ||||
| . . . | |||||
| 200 | 600 + 600 = 1200 |
| Total | = 6 + 12 + 18 + … + 1200 | ||||
| = 6 (1 + 2 + 3 + … + 200) | |||||
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| = 3 · 200 · 201 | |||||
| = 120,600 feet |
One student suggested that the Robot’s name might be Miles.