Understanding Average Speed Calculation
The question asks us to find the average speed for the entire journey undertaken by a person. The journey consists of two parts involving travel by bus and taxi, and also includes a period of rest.
Average speed is defined as the total distance covered divided by the total time taken to cover that distance. It's important to consider the entire duration of the journey, including any stops or rest periods, when calculating the overall average speed.
The formula for average speed is:
$$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $$
Journey Calculation Steps
Let's break down the journey and calculate the total distance and total time.
Step 1: Calculate the Total Distance
The person covered distance in two parts:
- Distance covered by bus = 40 km
- Distance covered by taxi = 20 km
Total Distance = Distance (Bus) + Distance (Taxi)
$$ \text{Total Distance} = 40 \text{ km} + 20 \text{ km} = 60 \text{ km} $$
Step 2: Calculate the Total Time
The total time includes the time spent traveling and the time spent resting:
- Time spent on bus = 70 minutes
- Rest time = 40 minutes
- Time spent on taxi = 40 minutes
Total Time = Time (Bus) + Rest Time + Time (Taxi)
$$ \text{Total Time} = 70 \text{ mins} + 40 \text{ mins} + 40 \text{ mins} = 150 \text{ minutes} $$
Step 3: Convert Total Time to Hours
Since the speed is usually measured in kilometers per hour (km/h), we need to convert the total time from minutes to hours.
We know that 1 hour = 60 minutes.
$$ \text{Total Time in hours} = \frac{150 \text{ minutes}}{60 \text{ minutes/hour}} $$
$$ \text{Total Time in hours} = 2.5 \text{ hours} $$
Step 4: Calculate the Average Speed
Now we can use the average speed formula with the total distance and total time in hours.
$$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time in hours}} $$
$$ \text{Average Speed} = \frac{60 \text{ km}}{2.5 \text{ hours}} $$
$$ \text{Average Speed} = 24 \text{ km/h} $$
Conclusion
The average speed for the whole journey, considering both travel and rest time, is 24 km/h.
Similar Questions
- A person travels two-fifth of a distance at a speed of 40 km/h and the remaining at a speed of 60 km/h. What is his average speed (in km/h) in the entire journey?
- A bus covers the first 80 km at a speed of 40 km/h. It covers the next 100 km at a speed of 50 km/h. What is its average speed?
- A man walks from point A to B at a speed of 15 km/h, but comes back from point B to A at a speed of 25 km/h. Find his average speed.
- While travelling from A to B, Raghav travels a quarter of the distance at 10 km/h, the next quarter of the distance at 15 km/h, the third quarter of the distance at 20 km/h, and the final quarter of the distance at 30 km/h. While travelling on exactly the same route, Manish travels for a quarter of the total time taken for his journey at 10 km/h, the next quarter of the total time taken for his journey at 15 km/h, the third quarter of the total time taken for his journey at 20 km/h, and the final quarter of the total time taken for his journey at 30 km/h. If the overall average speed of Raghav during his journey is given as y km/h, and that of Manish is given as z km/h, find the value of (z - y).
Reshma covers 45 km at a speed of 15 km/h by bicycle, 80 km at a speed of 40 km/h by car, and another 6 km at a speed of 2 km/h on foot. Find her average speed for the whole journey (correct to 2 decimal places).
- Dixit covers a certain distance by car, driving at the speed of 28 km/h and he returns to the starting point riding on a scooter at the speed of 36 km/h. Find the average speed (in km/h) for the whole journey.
- A train covers 40 km between two stations in 45 minutes. It covers another 30 km in 30 minutes and the remaining 20 km in 15 minutes. Find the average speed of the train in the whole journey.
- Arun is going from Delhi to Mumbai for a business trip. He travelled by train to reach Gandhinagar in 16 hours covering a distance of 920 km. After a break of 2 hours, he took another train from the same place to Mumbai, covering the distance in 12 hours. Arun took a total of 30 hours to cover the entire distance of 1478 km. What was the speed (in km/h) of the train going from Gandhinagar to Mumbai?
- What is the average speed of a car in km/h, if it travels 300 km in 4 h and remaining 150 km in 5 h?
Four cities P, Q, R and S are on the corner of the square and the side of a square is 75 km. A businessman travels from P to Q at 5 km/h, Q to R at 3 km/h, R to S at 5 km/h and S to P at 3 km/h. Find his average speed of the whole journey.
Important Questions from Average Speed
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?
To cover a distance of 144 km in 3.2 hours what should be the average speed of the car in meters/second?
A cylindrical road roller having a diameter of 1.5 m moves at a speed of 3km/h while levelling a road. How much length of the road will be levelled in 45 minutes?
