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 train goes from A to B at a speed of 40 km/hr and returns from B to A by the same route at 10 km/hr. The average speed (in km/hr) of the train during the two-way journey is:
- The distances between the points A, B and C are such that AB = 180 km and BC = 240 km. A traveler goes from A to B at 45 km/h, from B to C at 60 km/h, returns from C to B at 40 km/h, and finally from B to A at 30 km/h. Find the average speed (in km/h) for the entire journey.
- A man goes from place A to B at a speed of 12 km/h and returns from B to A at a speed of 3 km/h using the same route. The average speed (km/h) for the whole journey is:
- ______ is defined as the total path length travelled by an object divided by the total time interval during which the motion has taken place.
- An object travels the first \(200\text{ m}\) in \(20\text{ s}\) and the next \(200\text{ m}\) in \(30\text{ s}\). The average speed of the object is ______.
Simran rides a distance of 60 m in one minute and then returns along the same straight path. The average velocity of her ride is_________.
- 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.
A car travels 80 km at the speed of 20 km/hr and the next 30 km at the speed of 30 km/hr. What is the average speed?
- A car travels 120 km at 60 km/h, then 200 km at 80 km/h, but during the second segment, it experiences a total stoppage time of 20 minutes due to traffic. After that, it covers the final 150 km at 100 km/h. What is the average speed (in km/h, rounded off to one decimal place) of the car for the entire journey including stoppage times?
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?
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?
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?
