A horse covers a certain distance in 40 minutes if it runs at a speed of 60 km/hr. At what speed the horse can cover the same distance in 30 minutes?

Options

A. 86 km/hr
B. 84 km/hr
C. 82 km/hr
D. 80 km/hr

Answer

To solve the problem step by step, we need to determine the speed at which the horse can cover the same distance in 30 minutes, given that it covers that distance in 40 minutes at a speed of 60 km/hr.

### Step 1: Calculate the distance covered by the horse in 40 minutes.
- We know the formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Here, the speed \( S_1 = 60 \) km/hr and the time \( T_1 = 40 \) minutes.
- First, convert 40 minutes into hours:
\[ T_1 = \frac{40}{60} = \frac{2}{3} \text{ hours} \]
- Now, calculate the distance:
\[ \text{Distance} = 60 \text{ km/hr} \times \frac{2}{3} \text{ hours} = 40 \text{ km} \]

### Step 2: Find the speed required to cover the same distance in 30 minutes.
- We need to find the speed \( S_2 \) when the time \( T_2 = 30 \) minutes.
- First, convert 30 minutes into hours:
\[ T_2 = \frac{30}{60} = \frac{1}{2} \text{ hours} \]
- Now, use the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{40 \text{ km}}{\frac{1}{2} \text{ hours}} = 40 \text{ km} \times 2 = 80 \text{ km/hr} \]

### Conclusion
The speed at which the horse can cover the same distance in 30 minutes is **80 km/hr**.

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