To find the average speed of the person during the entire journey, we need to first calculate the total distance covered and the total time taken.
Step 1: Calculate the distance covered in the first part of the journey.
The person drove at a speed of 53 kmph for 2.5 hours. The distance covered in this part can be calculated using the formula:
\(Distance = Speed \times Time\)
\(Distance_1 = 53 \, \text{kmph} \times 2.5 \, \text{hours} = 132.5 \, \text{km}\)
Step 2: Calculate the distance covered in the second part of the journey.
After the first part, the person increased the speed by 28 kmph. So, the new speed is:
\(53 \, \text{kmph} + 28 \, \text{kmph} = 81 \, \text{kmph}\)
The distance covered in the next 1 hour is:
\(Distance_2 = 81 \, \text{kmph} \times 1 \, \text{hour} = 81 \, \text{km}\)
Step 3: Calculate the total distance and total time.
Total distance covered is the sum of distances from both parts:
\(\text{Total Distance} = 132.5 \, \text{km} + 81 \, \text{km} = 213.5 \, \text{km}\)
Total time taken is the sum of times taken for both parts:
\(\text{Total Time} = 2.5 \, \text{hours} + 1 \, \text{hour} = 3.5 \, \text{hours}\)
Step 4: Calculate the average speed.
The average speed is given by:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{213.5 \, \text{km}}{3.5 \, \text{hours}} = 61 \, \text{kmph}\)
Therefore, the average speed of the person during the entire journey is 61 kmph.
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.
