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 runs first 275 km at an average speed of 50 km/h and the next 315 km at an average speed of 70 km/h. What is the average speed ( in km/h) for the entire journey?
Akhil rides first 12 km at a speed of 16 km/h and further 6 km at a speed of 20 km/h. Find his average speed (in km/h).
Shyam drives his car 30 km at a speed of 45 km/h and, for the next 1 h 20 m, he drives it at a speed of 51 km/h. Find his average speed (in km/h) for the entire journey.
X and Y travel a distance of 90 km each such that the speed of Y is greater than that of X. The sum of their speeds is 100 km/h and the total time taken by both is 3 hours 45 minutes. The ratio of the speed of X to that of Y is:
If a man travels at \(\frac{1}{x}\) km/h on a journey and returns at \(\rm \frac{1}{x^2}\) km/h, then his average speed for the journey is:
