Understanding Time, Speed, and Distance Calculation

This question asks us to calculate the time saved when traveling a certain distance at an increased speed. To solve this, we first need to find the total distance covered. Then, we calculate the time it takes to cover the same distance at the new speed and finally find the difference in time, which is the time saved.

Step 1: Calculate the Distance Between Points A and B

We are given the initial speed and the time taken to cover the distance between points A and B.

• Initial Speed = 50 km/hr
• Initial Time = \(5 \frac{1}{2}\) hours

First, let's convert the initial time into a decimal or improper fraction for easier calculation.

\(5 \frac{1}{2} \text{ hours} = 5.5 \text{ hours}\) or \(\frac{11}{2} \text{ hours}\).

The formula relating distance, speed, and time is:

\(\text{Distance} = \text{Speed} \times \text{Time}\)

Using the initial values:

\(\text{Distance} = 50 \, \text{km/hr} \times 5.5 \, \text{hours}\)

\(\text{Distance} = 275 \, \text{km}\)

So, the distance between points A and B is 275 km.

Step 2: Calculate the New Speed

The question states that the speed is increased by 5 km/hr.

• Initial Speed = 50 km/hr
• Increase in Speed = 5 km/hr

New Speed = Initial Speed + Increase in Speed

New Speed = 50 km/hr + 5 km/hr

New Speed = 55 km/hr

Step 3: Calculate the Time Taken at the New Speed

Now we use the calculated distance and the new speed to find the time taken.

• Distance = 275 km
• New Speed = 55 km/hr

Using the formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\):

\(\text{New Time} = \frac{275 \, \text{km}}{55 \, \text{km/hr}}\)

\(\text{New Time} = 5 \, \text{hours}\)

So, at the increased speed of 55 km/hr, the journey would take 5 hours.

Step 4: Calculate the Time Saved

The time saved is the difference between the initial time and the new time.

• Initial Time = 5.5 hours
• New Time = 5 hours

\(\text{Time Saved} = \text{Initial Time} - \text{New Time}\)

\(\text{Time Saved} = 5.5 \, \text{hours} - 5 \, \text{hours}\)

\(\text{Time Saved} = 0.5 \, \text{hours}\)

Step 5: Convert Time Saved to Minutes

The options are given in minutes. We need to convert 0.5 hours into minutes.

There are 60 minutes in 1 hour.

\(\text{Time Saved (minutes)} = \text{Time Saved (hours)} \times 60 \, \text{minutes/hour}\)

\(\text{Time Saved (minutes)} = 0.5 \, \text{hours} \times 60 \, \text{minutes/hour}\)

\(\text{Time Saved (minutes)} = 30 \, \text{minutes}\)

Thus, 30 minutes would be saved if the speed is increased by 5 km/hr.

Revision Table: Time, Speed, and Distance Concepts

Additional Information: Speed Calculation Tips

• Always ensure units are consistent when using the formulas (e.g., if speed is in km/hr, time should be in hours and distance in km).
• Converting between units like hours and minutes (1 hour = 60 minutes) is crucial for time, speed, and distance problems.
• Increasing speed reduces the time taken for a fixed distance, while decreasing speed increases the time taken.
• Understanding fractional or decimal time representations (like \(5 \frac{1}{2}\) hours = 5.5 hours) is important.