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Let the length of one piece of the rope be \( x \) yards.

According to the problem, the other piece is 4 yards longer than 8 times the first piece. So, the length of the second piece will be \( 8x + 4 \) yards.

The total length of the rope is 40 yards. Therefore, we can write the equation:

\[
x + (8x + 4) = 40
\]

Now, solve for \( x \):

1. Combine like terms:
\[
x + 8x + 4 = 40
\]
\[
9x + 4 = 40
\]

2. Subtract 4 from both sides:
\[
9x = 36
\]

3. Divide by 9:
\[
x = 4
\]

Thus, the length of one piece is \( 4 \) yards. The length of the other piece, using the expression \( 8x + 4 \), is:

\[
8(4) + 4 = 32 + 4 = 36 \text{ yards}.
\]

So, the two pieces are 4 yards and 36 yards.

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. What if the rope was 50 yards and the condition remained the same?
2. How would the problem change if the second piece was 3 yards longer instead of 4 yards longer?
3. What would happen if both pieces were equal in length?
4. How would you solve if the second piece was 6 times the length of the first piece?
5. Can you solve the problem algebraically if the total length was unknown?

**Tip:** When dealing with word problems, defining variables clearly and translating the words into equations is key to solving them accurately.

A 40-yard rope is cut into two pieces such that one piece is four yards longer than eight times the other piece. Determine the length of each piece.

Learn how to solve a problem where a 40-yard rope is cut into two pieces, with one piece being four yards longer than eight times the other. This problem involves key algebraic concepts and is suitable for students in Grades 7-9.

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