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

Let's solve the problem step by step.

We are given:

- The total distance from point P to point R is 800 yards.
- The distance from P to Q is 4 times the distance from Q to R.
- Olivia says: "It is 600 yards from point P to point Q."

We are asked to explain why Olivia is not correct.

---

Step 1: Define variables

Let:
- $ x $ = distance from Q to R

Then:
- Distance from P to Q = $ 4x $ (since it's 4 times the distance from Q to R)

Total distance from P to R = $ PQ + QR = 4x + x = 5x $

But we know:
$$
5x = 800 \text{ yards}
$$

Solve for $ x $:
$$
x = \frac{800}{5} = 160 \text{ yards}
$$

So:
- $ QR = 160 $ yards
- $ PQ = 4x = 4 \times 160 = 640 $ yards

---

Step 2: Check Olivia’s claim

Olivia says: "It is 600 yards from P to Q."

But we just calculated that PQ = 640 yards, not 600.

So, Olivia is incorrect.

---

Final Answer:

Olivia is not correct because the distance from P to Q is 640 yards, not 600 yards.

We know this because:
- The total distance from P to R is 800 yards.
- Since PQ is 4 times QR, we divide the total into 5 equal parts: 800 ÷ 5 = 160 yards per part.
- So PQ = 4 × 160 = 640 yards.

Therefore, Olivia's statement of 600 yards is too low.

---

✔ Answer:
*Olivia is not correct because the distance from P to Q is 640 yards, not 600 yards. The total distance from P to R is 800 yards, and since PQ is 4 times QR, PQ must be 640 yards.*