Final answer:
The shortest distance from the end of the rope with both red and green tape is the least common multiple of 3 and 8, which is 24 inches.
Step-by-step explanation:
The question involves finding the least common multiple (LCM) of two distances at which red and green tapes are placed along a rope. The red tape is placed every 3 inches while the green tape is placed every 8 inches. To find the shortest distance from the end of the rope where both red and green tape will be located, we must determine the LCM of 3 and 8.
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
- Multiples of 8: 8, 16, 24, ...
By comparing the multiples of 3 and 8, we find that 24 is the smallest number that appears in both lists. Therefore, the shortest distance from the end of the rope where there will be both red and green tape is 24 inches.