Final answer:
The length of the shorter piece of pipe is found to be 3.67 inches by setting up an equation and solving for x. The longer piece, being five times the shorter piece, measures 18.33 inches.
Step-by-step explanation:
The student's question involves the division of a 22-inch pipe into two unequal pieces, where one piece is five times longer than the other. To solve for the shorter piece, let's denote the length of the shorter piece as x inches. Consequently, the longer piece would be 5x inches. Since the total length of the pipe is given as 22 inches, we can set up the equation x + 5x = 22.
Combining the like terms, we get 6x = 22. To find the value of x, we divide both sides of the equation by 6, which gives us x = 22 / 6. Simplifying this, x = 3.6667 inches, which can be rounded to 3.67 inches for the shorter piece.
Now, the length of the longer piece is five times that of the shorter one, which is 5 * 3.67 inches. Multiplying this out, the longer piece measures 18.35 inches, which can be rounded to 18.33 inches for a more simplified answer.
Therefore, the longer piece is 18.33 inches long.