A truck driver drove 60 km/h for three hours. Then he stopped for one hour and did not go anywhere. Then, he drove four more hours at 60 km/h. What was the driver's average speed (in km/h)?
52.5
Understanding Average Speed Calculation
The question asks us to find the average speed of a truck driver over a journey that includes different phases: driving at a constant speed and stopping for a period. To calculate the average speed, we need to use the formula:
\(\text{Average Speed} = \frac{\text{Total Distance Traveled}}{\text{Total Time Taken}}\)
It's important to account for all parts of the journey in both the total distance and the total time.
Step-by-Step Calculation of Truck Driver's Average Speed
Let's break down the truck driver's journey into segments to find the total distance and total time.
Calculating Total Distance
- Segment 1: The driver drove at 60 km/h for three hours.
- Distance in Segment 1 = Speed × Time = 60 km/h × 3 hours = 180 km.
- Segment 2: The driver stopped for one hour. Stopping means the speed is 0 km/h.
- Distance in Segment 2 = Speed × Time = 0 km/h × 1 hour = 0 km.
- Segment 3: The driver drove four more hours at 60 km/h.
- Distance in Segment 3 = Speed × Time = 60 km/h × 4 hours = 240 km.
Total Distance Traveled = Distance in Segment 1 + Distance in Segment 2 + Distance in Segment 3
Total Distance = 180 km + 0 km + 240 km = 420 km.
Calculating Total Time
The total time taken for the entire journey is the sum of the durations of all segments.
- Time in Segment 1 = 3 hours.
- Time in Segment 2 (Stop) = 1 hour.
- Time in Segment 3 = 4 hours.
Total Time Taken = Time in Segment 1 + Time in Segment 2 + Time in Segment 3
Total Time = 3 hours + 1 hour + 4 hours = 8 hours.
Calculating Average Speed
Now we can use the total distance and total time in the average speed formula.
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
\(\text{Average Speed} = \frac{420 \text{ km}}{8 \text{ hours}}\)
\(\text{Average Speed} = 52.5 \text{ km/h}\)
The truck driver's average speed for the entire journey was 52.5 km/h.
| Segment | Speed (km/h) | Time (hours) | Distance (km) |
|---|---|---|---|
| 1 | 60 | 3 | 180 |
| 2 (Stop) | 0 | 1 | 0 |
| 3 | 60 | 4 | 240 |
| Total | - | 8 | 420 |
Average Speed = \(\frac{\text{Total Distance}}{\text{Total Time}} = \frac{420}{8} = 52.5 \text{ km/h}\)
Revision Table: Key Concepts in Speed Calculation
| Concept | Formula | Notes |
|---|---|---|
| Speed | \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\) | Rate of motion, scalar quantity |
| Distance | \(\text{Distance} = \text{Speed} \times \text{Time}\) | How far an object traveled |
| Time | \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\) | Duration of motion |
| Average Speed | \(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\) | Applies over an entire journey |
| Velocity | \(\text{Velocity} = \frac{\text{Displacement}}{\text{Time}}\) | Speed with direction, vector quantity |
Additional Information on Average Speed vs. Instantaneous Speed
It's helpful to understand the difference between average speed and instantaneous speed.
- Instantaneous Speed: This is the speed of an object at a specific moment in time. A car's speedometer shows its instantaneous speed. In this problem, the driver's instantaneous speed was 60 km/h during the driving periods and 0 km/h during the stop.
- Average Speed: This is the total distance covered divided by the total time taken for the entire trip. It smooths out variations in speed during the journey, including stops or changes in speed. The average speed is not necessarily equal to the average of the instantaneous speeds unless the instantaneous speed was constant throughout the entire duration (which was not the case here because of the stop).
In this truck driver problem, even though the driving speed was constant at 60 km/h when the truck was moving, the average speed over the entire 8-hour period was lower (52.5 km/h) because the total time included a period where no distance was covered.
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.
