Understanding the Bus Journey Problem

This problem involves calculating the speed required for a bus to cover the same distance in a different amount of time. We are given the initial speed and time, and we need to find the new speed for a shorter time duration.

Calculating the Total Distance

First, we need to determine the total distance of the journey. The formula relating distance, speed, and time is:

Distance = Speed × Time

Given:

• Initial Speed ($S_1$) = 66 km/hr
• Initial Time ($T_1$) = 15 hours

Using the formula, the distance ($D$) is:

$ D = S_1 \times T_1 $

$ D = 66 \text{ km/hr} \times 15 \text{ hours} $

$ D = 990 \text{ km} $

So, the total distance of the journey is 990 kilometers.

Determining the New Speed

Now, we need to find the speed required to cover this same distance (990 km) in a new, shorter time.

Given:

• Distance ($D$) = 990 km
• New Time ($T_2$) = 5 hours

The formula to calculate the new speed ($S_2$) is:

Speed = Distance / Time

$ S_2 = \frac{D}{T_2} $

$ S_2 = \frac{990 \text{ km}}{5 \text{ hours}} $

$ S_2 = 198 \text{ km/hr} $

Therefore, the bus should travel at a speed of 198 km/hr to complete the same journey in 5 hours.

Summary of Calculation

The problem highlights the inverse relationship between speed and time when the distance is constant. To cover the same distance in less time, the speed must increase proportionally.

Initial Speed ($S_1$) = 66 km/hr, Initial Time ($T_1$) = 15 hours

Distance ($D$) = $66 \times 15 = 990$ km

New Time ($T_2$) = 5 hours

New Speed ($S_2$) = $\frac{990}{5} = 198$ km/hr