A car has to cover 125 kms in 5 hours. What will be the average speed of the car if it has covered 90 kms in the first 3 hours?
25 km/h
Calculating Car's Average Speed for the Entire Journey
This problem asks us to find the average speed of a car over a complete journey. We are given the total distance the car needs to cover and the total time allocated for the journey. We are also given information about the speed during the initial part of the journey, but this information is not required to calculate the average speed for the entire journey.
The average speed of an object is defined as the total distance covered divided by the total time taken for the journey.
The formula for average speed is:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
Given Information:
- Total distance to be covered = 125 kms
- Total time allocated = 5 hours
- Distance covered in the first 3 hours = 90 kms (This information is extra for calculating the total average speed)
- Time taken for the first 90 kms = 3 hours
Step-by-Step Calculation of Average Speed
To find the average speed for the entire journey, we need the total distance and the total time for the entire journey.
- Identify the total distance: The car has to cover a total of 125 kms.
- Identify the total time: The journey is to be completed in 5 hours.
- Apply the average speed formula:
\(\text{Average Speed} = \frac{125 \text{ kms}}{5 \text{ hours}}\)
Now, perform the division:
\(\text{Average Speed} = \frac{125}{5} \text{ km/h}\)
\(\text{Average Speed} = 25 \text{ km/h}\)
Therefore, the average speed of the car for the entire journey of 125 kms in 5 hours is 25 km/h.
The information about covering 90 kms in the first 3 hours tells us that the car's average speed during the first part was \(90 \text{ kms} / 3 \text{ hours} = 30 \text{ km/h}\). However, this does not change the overall average speed needed to cover 125 kms in 5 hours.
Average Speed vs. Speed over Segments
It's important to distinguish between average speed over the entire journey and the average speed over a specific part of the journey. The question specifically asks for the average speed over the total time frame (5 hours) for the total distance (125 kms).
| Journey Segment | Distance | Time | Average Speed (Distance/Time) |
|---|---|---|---|
| First Part | 90 kms | 3 hours | \(90/3 = 30 \text{ km/h}\) |
| Remaining Part | \(125 - 90 = 35 \text{ kms}\) | \(5 - 3 = 2 \text{ hours}\) | \(35/2 = 17.5 \text{ km/h}\) |
| Entire Journey | 125 kms | 5 hours | \(125/5 = 25 \text{ km/h}\) |
As the table shows, the average speed varies over different segments of the journey. However, the average speed for the entire 125 km journey over 5 hours is fixed at 25 km/h, regardless of how the speed changed during intermediate segments.
Revision Table: Key Concepts for Speed Problems
| Concept | Formula | Units (Common) | Notes |
|---|---|---|---|
| Speed | \(\frac{\text{Distance}}{\text{Time}}\) | km/h, m/s, mph | Rate of change of distance with time |
| Average Speed | \(\frac{\text{Total Distance}}{\text{Total Time}}\) | km/h, m/s, mph | Average rate over an entire journey |
| Distance | \(\text{Speed} \times \text{Time}\) | km, m, miles | Length of the path covered |
| Time | \(\frac{\text{Distance}}{\text{Speed}}\) | hours, seconds, minutes | Duration of the journey |
Additional Information on Average Speed Calculations
When dealing with speed, distance, and time problems, understanding the relationship between these three is crucial. Average speed provides an overall measure of how fast an object traveled over a certain duration, even if its instantaneous speed varied throughout the journey.
- If an object travels at different speeds for different durations or distances, the average speed is calculated using the total distance and total time, not by averaging the speeds directly (unless time intervals are equal).
- In cases where an object travels at speed \(v_1\) for time \(t_1\) and speed \(v_2\) for time \(t_2\), the total distance is \(d_1 + d_2 = (v_1 \times t_1) + (v_2 \times t_2)\), and the total time is \(t_1 + t_2\). The average speed is then \(\frac{(v_1 \times t_1) + (v_2 \times t_2)}{t_1 + t_2}\).
- In cases where an object travels distance \(d_1\) at speed \(v_1\) and distance \(d_2\) at speed \(v_2\), the time taken for each segment is \(t_1 = d_1/v_1\) and \(t_2 = d_2/v_2\). The total distance is \(d_1 + d_2\) and the total time is \(\frac{d_1}{v_1} + \frac{d_2}{v_2}\). The average speed is then \(\frac{d_1 + d_2}{\frac{d_1}{v_1} + \frac{d_2}{v_2}}\).
For this particular problem, the most straightforward approach is to use the total given distance and total given time because the question asks for the average speed over the entire defined journey.
Important Questions from Average Speed
A person covers a certain distance at the speed of 60 kmph and returns to the starting point at a speed of 40 kmph . Find the average speed (in km/hour) of the person for the whole journey.
A train runs at a speed of 28 kmph for 4 hours and 30 kmph for 5 hours and the remaining 40 kms in one hour. What is the average speed per hour?
Kapil travels for 4.5 hours at a speed of 50 km / h and 7.5 hours at a speed of 70 km / h. At the end of it, he finds that he covered only 6/7 of the total distance. At what average speed should he travel so that the remaining distance traveled in 5 hours?
An express train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long it take to reach its destination 600 km from the starting point?
A scooter from P to Q travels at 40 km/h and from Q to P at 30 km/h. What is the average speed of the scooter?
