35 Math Questions For 5th Graders: Worked Examples - Free Printable

To solve the problem and explain why Olivia is not correct, let's break it down step by step.

Step 1: Understand the given information

- The total distance from point \( P \) to point \( R \) is 800 yards.
- The distance from point \( P \) to point \( Q \) is 4 times the distance from point \( Q \) to point \( R \).

Let:
- \( PQ \) be the distance from \( P \) to \( Q \).
- \( QR \) be the distance from \( Q \) to \( R \).

From the problem, we know:
1. \( PQ + QR = 800 \) yards.
2. \( PQ = 4 \times QR \).

Step 2: Set up the equations

Using the second piece of information, we can express \( PQ \) in terms of \( QR \):
\[ PQ = 4 \times QR. \]

Substitute \( PQ = 4 \times QR \) into the first equation:
\[ 4 \times QR + QR = 800. \]

Step 3: Solve for \( QR \)

Combine like terms:
\[ 5 \times QR = 800. \]

Divide both sides by 5:
\[ QR = \frac{800}{5} = 160. \]

Step 4: Find \( PQ \)

Now that we know \( QR = 160 \) yards, we can find \( PQ \) using the relationship \( PQ = 4 \times QR \):
\[ PQ = 4 \times 160 = 640. \]

Step 5: Compare with Olivia's statement

Olivia says that the distance from point \( P \) to point \( Q \) is 600 yards. However, we have calculated that:
\[ PQ = 640 \text{ yards}. \]

Step 6: Explain why Olivia is incorrect

Olivia's statement is incorrect because the actual distance from \( P \) to \( Q \) is 640 yards, not 600 yards. This discrepancy arises because Olivia did not correctly apply the relationship between \( PQ \) and \( QR \).

Final Answer

\[
\boxed{\text{Olivia is incorrect because the actual distance from } P \text{ to } Q \text{ is 640 yards, not 600 yards.}}
\]