Question 52: Cyclist in the Park

 

Question:
A park is 1500 m long and 750 m wide. A cyclist has to take four rounds of this park. How much time will he take at a speed of 4.5 km/h?
Options: (a) 40 h (b) 20 h (c) 10 h (d) 4 h

---

Step 1: Understanding the Problem Like a Kid

Imagine a big rectangle-shaped park. The cyclist rides around the park’s boundary — that’s like walking along the edge of a chocolate bar. To find out how far he will ride, we need the perimeter of the park.

Formula for perimeter of a rectangle:

$$\text{Perimeter} = 2 \times (\text{Length} + \text{Width})$$

Here:

• Length = 1500 m

• Width = 750 m

So,

$$\text{Perimeter} = 2 \times (1500 + 750) = 2 \times 2250 = 4500 \text{ m}$$

Think of it like: if you walk around the edge of your school 2 times (like 2 rectangles stuck together), you know the total path.

---

Step 2: Distance for 4 Rounds

The cyclist has to go 4 rounds, so multiply the perimeter by 4:

$$\text{Total distance} = 4 \times 4500 = 18000 \text{ m}$$

Convert meters to kilometers because the speed is in km/h:

$$18000 \text{ m} = 18 \text{ km} \quad (\text{divide by 1000})$$

---

Step 3: Time = Distance ÷ Speed

We know from life: time = how far you go ÷ how fast you go.

$$\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{18}{4.5} = 4 \text{ hours}$$

✅ Answer: (d) 4 h

---

Fast Calculation Tip

1. Round numbers if they are tricky. Example: 4.5 km/h is easy to see as “4.5” → 18 ÷ 4.5 = 4.

2. Match units first: If distance is in meters and speed in km/h, convert meters to km first.

3. Think in steps: Perimeter → Total Distance → Time. Breaking problems into small steps makes it faster.

---

Analogy for Kids:

Think of a race track (the park). Each lap is like a slice of chocolate. If you eat 4 slices, you know the total chocolate you ate. Then, if you eat 1 slice in half an hour, you can easily find out how long it will take to finish all slices!