This problem is based on Dan Meyer's 3 Act Play called Ditch Diggers. In the video, you have to predict whether or not the ditch diggers will meet, and if so, on what day. In Act 2, coordinates are provided, and in Act 3, the solution is shown. We are using revised problems with the following coordinates.
SCENARIO 1:
Digger A (Let's call him Albert)
day 0 (0, 0)
day 1 (1, 1)
day 2 (2, 2)
day 3 (3, 3)
day 4
day 5...
Digger B: (Let's call him Barney)
day 0 (19, 36)
day 1 (18, 33)
day 2 (17, 30)
day 3 (16, 27)
day 4
day 5...
SCENARIO 2:
Digger C: (Let's call him Clyde)
day 0 (2, 1)
day 1 (4, 5)
day 2 (6, 9)
day 3 (8, 13)
day 4
day 5...
Digger D: (Let's call him Daryl)
day 0 (22, 38)
day 1 (21, 36)
day 2 (20, 34)
day 3 (19, 32)
day 4
day 5...
Our questions are:
- Will the diggers meet in each scenario?
- If they meet, on which day?
- If they don't meet, who should adjust and on which day?
Our assumptions are:
- The diggers keep the same rate (or slope) each day.
- The diggers don't stop for weekends and holidays!
