Food is available at the end of a cobbled road. Robby, the rabbit, takes a jump of 4 each time. Deeku, the deer, takes a jump of 6 each time. They both start at 0. Will both Robby and Deeku reach the food? Who will reach first? How do you know? Explain your answer.
Both Robby and Deeku will reach the food if the food is placed at a common multiple of 4 and 6.
Common multiples of 4 and 6: 12, 24, 36, 48, ...
Robby's positions (jump of 4): 4, 8, 12, 16, 20, 24, ...
Deeku's positions (jump of 6): 6, 12, 18, 24, ...
If food is at position 12: Deeku reaches in 2 jumps Robby reaches in 3 jumps ∴ Deeku reaches first.
If food is at position 24: Deeku reaches in 4 jumps Robby reaches in 6 jumps ∴ Deeku reaches first.
Conclusion: Deeku will always reach first at any common multiple because Deeku takes fewer jumps to reach the same position.
Explanation
The chapter uses the concept of common multiples through animal jumps. The rabbit jumps in multiples of 4 (4, 8, 12, 16, 20, 24...) and the deer jumps in multiples of 6 (6, 12, 18, 24...). The common multiples of 4 and 6 are 12, 24, 36, 48... where both animals land. To determine who reaches first, we compare the number of jumps: at position 12, rabbit needs 3 jumps (12÷4=3) while deer needs 2 jumps (12÷6=2).
Solution Steps
Identify that both animals reach the food if it's at a common multiple of 4 and 6.
List the common multiples of 4 and 6: 12, 24, 36, 48, ...
List Robby's positions (multiples of 4): 4, 8, 12, 16, 20, 24, ...
List Deeku's positions (multiples of 6): 6, 12, 18, 24, ...
At position 12: Deeku needs 2 jumps, Robby needs 3 jumps → Deeku reaches first.
At position 24: Deeku needs 4 jumps, Robby needs 6 jumps → Deeku reaches first.
Conclude: Deeku always reaches first at any common multiple because he takes fewer jumps.