Calculating New Bus Speed for Reduced Journey Time

This problem involves understanding the relationship between speed, distance, and time. The core formula connecting these three is:

Distance = Speed × Time

We are given the initial speed of the bus and the time it took to complete a journey. We need to find the new speed required to cover the exact same distance but in a shorter amount of time.

Step 1: Calculate the Total Distance of the Journey

First, let's find the total distance the bus travelled using the initial information:

• Initial Speed = $95 \text{ km/hr}$
• Initial Time = $10 \text{ hours}$

Using the formula, Distance = Speed × Time:

Distance = $95 \frac{\text{km}}{\text{hr}} \times 10 \text{ hr}$

Distance = $950 \text{ km}$

So, the total distance of the journey is 950 kilometers.

Step 2: Calculate the Required Speed for the New Time

Now, the bus needs to cover the same distance (950 km) but in a new, shorter time frame.

• Distance = $950 \text{ km}$
• New Time = $5 \text{ hours}$

To find the new speed, we rearrange the formula: Speed = Distance / Time.

New Speed = $\frac{950 \text{ km}}{5 \text{ hr}}$

New Speed = $190 \frac{\text{km}}{\text{hr}}$

Conclusion

To cover the same distance of 950 km in just 5 hours, the bus must travel at a speed of 190 km/hr. This makes sense because to cover the same distance in half the time, the speed needs to be doubled.