A horse completes a 100-m diameter circular track thrice in 20 minutes. What is the speed of the horse?

To determine the speed of the horse, we need to find the total distance covered by the horse and then divide it by the total time taken.

### Step 1: Calculate the circumference of the circular track.
The diameter of the track is given as 100 meters. The circumference \(C\) of a circle is calculated using the formula:
\[
C = \pi \times d
\]
where \(d\) is the diameter.

Substituting the given diameter:
\[
C = \pi \times 100 \, \text{m} \approx 3.1416 \times 100 \, \text{m} \approx 314.16 \, \text{m}
\]

### Step 2: Calculate the total distance covered.
The horse completes 3 laps around the track. So, the total distance \(D\) covered is:
\[
D = 3 \times C = 3 \times 314.16 \, \text{m} \approx 942.48 \, \text{m}
\]

### Step 3: Convert the time into seconds.
The horse takes 20 minutes to complete the 3 laps. To convert minutes into seconds:
\[
T = 20 \times 60 \, \text{seconds} = 1200 \, \text{seconds}
\]

### Step 4: Calculate the speed.
Speed \(v\) is given by the formula:
\[
v = \frac{\text{Distance}}{\text{Time}} = \frac{D}{T}
\]
Substituting the values:
\[
v = \frac{942.48 \, \text{m}}{1200 \, \text{s}} \approx 0.7854 \, \text{m/s}
\]

So, the speed of the horse is approximately **0.7854 meters per second**.

Would you like further details or have any questions?

Here are some related questions:
1. What would be the speed if the horse completed the track in 15 minutes?
2. How would the speed change if the diameter of the track was 150 meters?
3. What is the time taken if the horse runs at a speed of 1 m/s?
4. How much distance would the horse cover in 10 minutes at the current speed?
5. How many laps would the horse complete in 30 minutes at the current speed?
6. What is the relationship between the diameter of the track and the speed of the horse?
7. If the horse increased its speed by 50%, what would the new speed be?
8. How would the speed change

Explore how to calculate the speed of a horse running on a 100-meter diameter circular track. Learn the steps involved in determining the speed using the circumference formula and converting time units. Suitable for Grades 7-9.

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