Problem

The 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 $R$.
Olivia says,
It is 600 yards from point $P$ to point Q.

Explain why Olivia is not correct.

Answer

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Answer

\(\boxed{\text{Therefore, Olivia's statement is not correct.}}\)

Steps

Step 1 :Given that the distance from point P to point R is 800 yards.

Step 2 :It is also given that the distance from point P to point Q is 4 times the distance from point Q to point R.

Step 3 :Olivia claims that the distance from point P to point Q is 600 yards.

Step 4 :If Olivia's claim is correct, then the distance from point Q to point R would be \(\frac{600}{4} = 150\) yards.

Step 5 :This would mean that the total distance from point P to point R (P to Q + Q to R) would be \(600 + 150 = 750\) yards.

Step 6 :This contradicts the given information that the distance from point P to point R is 800 yards.

Step 7 :\(\boxed{\text{Therefore, Olivia's statement is not correct.}}\)

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