Final answer:
The total length of the original string is 8.0 meters. If the string's length were doubled, the total length would be 16.0 meters.
Step-by-step explanation:
The student is asking about the length of a string that has been cut into three pieces with a certain ratio between the lengths of the pieces.
To solve this, let's denote the length of the third (shortest) piece as x. According to the problem, the second piece is thrice as long as the third piece, so its length is 3x. The first piece is twice as long as the second piece, which means it is 2 * 3x = 6x.
The longest piece, which is the first piece, measures 4.8 meters, so 6x = 4.8 m. Solving for x gives us the length of the third piece, and then we can find the total length of the string.
6x = 4.8 m → x = 0.8 m.
The second piece is 3x, which equals 3 * 0.8 m = 2.4 m.
Therefore, the total length of the string is the sum of the lengths of all three pieces:
Total length = First piece + Second piece + Third piece
= 4.8 m + 2.4 m + 0.8 m
= 8.0 meters.
For part (c) of the problem, if the string was twice as long, the lengths of the individual pieces would double, resulting in a total string length of 16.0 meters.