Final answer:
To find the difference between the longest and shortest possible combinations of the pipe sections, divide the 12-yard-long pipe into three equal sections, cut two sections in half, and one of the halves into thirds. The longest possible combination is 8 yards, while the shortest possible combination is 6 and 2/3 yards. The difference between the longest and shortest combinations is 6 and 2/3 yards.
Step-by-step explanation:
To find the longest and shortest possible combinations, we need to determine the lengths of each section after the pipe is cut multiple times. First, we divide the 12-yard-long pipe into three equal sections, resulting in each section being 4 yards long. Then, two of these resulting sections are cut in half, making each half 2 yards long. One of these halves is cut into thirds, making each third 2/3 yards long.
Now, let's calculate the lengths of the combinations:
- The longest possible combination is obtained by choosing the two longest sections. So, we combine two 4-yard sections, resulting in a total length of 8 yards.
- The shortest possible combination is obtained by choosing the two shortest sections. So, we combine two 2/3 yard sections, resulting in a total length of 4/3 yards.
To find the difference between the longest and shortest combinations, we subtract the shortest length from the longest length: 8 yards - 4/3 yards. To simplify this subtraction, we need to convert 8 yards to thirds. Since 1 yard equals 3 thirds, 8 yards equals 8 * 3 = 24 thirds. Now, the subtraction becomes: 24 thirds - 4/3 yards. To subtract fractions, we need a common denominator, which in this case is 3. So, the subtraction becomes: (24 - 4)/3 thirds = 20/3 thirds. Finally, we convert this back to yards by dividing 20 by 3: 20/3 yards = 6 and 2/3 yards.
Therefore, the difference between the longest possible and shortest possible combinations is 6 and 2/3 yards.