f a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actualdistance travelled by him is

1. Break Down the Problem

Let the actual distance walked by the person be $D$ km. To solve the problem, we can set up the relationship using the time taken to cover the distances at both speeds.

2. Relevant Concepts

1. Distance, Speed, and Time relationship: $\text{Distance} = \text{Speed} \times \text{Time}$

2. If the person travels at 10 km/hr, the time taken to travel $D$ km is: $\text{Time at 10 km/hr} = \frac{D}{10}$

3. If the person travels at 14 km/hr, the distance he would cover in the same time plus 20 km is: $\text{Time at 14 km/hr} = \frac{D + 20}{14}$

3. Analysis and Detail

Since the time taken at both speeds is the same, we can set the equations equal to each other: $\frac{D}{10} = \frac{D + 20}{14}$

Next, we will cross-multiply to solve for $D$: $14D = 10(D + 20)$

Expanding the right side gives: $14D = 10D + 200$

Rearranging the equation: $14D - 10D = 200$ $4D = 200$ $D = 50$

4. Verify and Summarize

We can verify the solution by checking the times with both speeds:

• Time at 10 km/hr for 50 km: $\text{Time} = \frac{50}{10} = 5 \text{ hours}$

• Distance at 14 km/hr in the same time plus 20 km: $\text{Distance} = 14 \times 5 = 70 \text{ km}$

• The difference: $70 - 50 = 20 \text{ km}$

The calculations confirm that the actual distance travelled by him is correct.

Final Answer

The actual distance travelled by him is 50 km.