Car Journey Average Speed Calculation
The problem asks for the average speed of a car over a journey with different speeds for different distances.
Understanding Average Speed Formula
The fundamental formula for average speed is:
\( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \)
Calculating Total Distance
The car travels three segments:
- Segment 1: \(x\) km
- Segment 2: \(x\) km
- Segment 3: \(2x\) km
Total Distance = \(x + x + 2x = 4x\) km.
Calculating Time for Each Segment
We use the formula: \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \)
- Time for Segment 1 (\(t_1\)): \( \frac{x \text{ km}}{40 \text{ km/hr}} = \frac{x}{40} \) hours.
- Time for Segment 2 (\(t_2\)): \( \frac{x \text{ km}}{60 \text{ km/hr}} = \frac{x}{60} \) hours.
- Time for Segment 3 (\(t_3\)): \( \frac{2x \text{ km}}{80 \text{ km/hr}} = \frac{x}{40} \) hours.
Calculating Total Time
Sum the times for all segments:
\( \text{Total Time} (T) = t_1 + t_2 + t_3 = \frac{x}{40} + \frac{x}{60} + \frac{x}{40} \)
To add these fractions, find a common denominator, which is 120:
\( T = \frac{3x}{120} + \frac{2x}{120} + \frac{3x}{120} = \frac{3x + 2x + 3x}{120} = \frac{8x}{120} \)
Simplify the fraction:
\( T = \frac{x}{15} \text{ hours} \)
Calculating Average Speed
Now, apply the average speed formula using the calculated total distance and total time:
\( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{4x \text{ km}}{\frac{x}{15} \text{ hours}} \)
\( \text{Average Speed} = 4x \times \frac{15}{x} = 4 \times 15 = 60 \text{ km/hr} \)
Conclusion
The average speed for the whole journey is 60 km/hr.
Similar Questions
- A person drove at 53 kmph for 2.5 hours, then increased his speed by 28 kmph, and reached the destination in another hour. Find the average speed (in kmph) of the person during the entire journey.
Important Questions from Average Speed
A car covers the first 41 km of its journey in 45 min and covers the remaining 23 km in 35 min. What is the average speed (in m/sec) of the car?
Akhil drives a car from his home to office at an average speed of 50 km/h and reaches office 10 minutes early. But one day due to some problem with the car, he could drive at an average speed of 30 km/h only and reached office 10 minutes late. How far is his office from home ?
During a flight of 900 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 300 km/h and the time of flight increased by 30 min. The original duration of the flight was :
If a man travels from A to B at a speed of 50 km/h and returns by increasing his speed by 40%, then find his average speed (to 2 decimal places) for both the trips.
A man travels a distance of 420 km by train which moves at the speed of 75 km/h and returns back by car at the speed of 50 km/h. Find his average speed for the whole journey.
