A truck travels 40 km in first hour and 50 km in second hour. What is the average speed of truck?
45 km/hr
Calculating Average Speed of a Truck
The question asks us to find the average speed of a truck that travels different distances in different hours.
Average speed is defined as the total distance traveled divided by the total time taken for the journey.
The formula for average speed is:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
Step-by-Step Calculation
Let's break down the information given in the problem:
- Distance covered in the first hour: 40 km
- Time taken for the first part: 1 hour
- Distance covered in the second hour: 50 km
- Time taken for the second part: 1 hour
1. Calculate Total Distance
The total distance is the sum of the distances covered in each hour.
\(\text{Total Distance} = \text{Distance in hour 1} + \text{Distance in hour 2}\)
\(\text{Total Distance} = 40 \text{ km} + 50 \text{ km}\)
\(\text{Total Distance} = 90 \text{ km}\)
2. Calculate Total Time
The total time is the sum of the times taken for each part of the journey.
\(\text{Total Time} = \text{Time in hour 1} + \text{Time in hour 2}\)
\(\text{Total Time} = 1 \text{ hour} + 1 \text{ hour}\)
\(\text{Total Time} = 2 \text{ hours}\)
3. Calculate Average Speed
Now, we use the formula for average speed with the calculated total distance and total time.
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
\(\text{Average Speed} = \frac{90 \text{ km}}{2 \text{ hours}}\)
\(\text{Average Speed} = 45 \text{ km/hr}\)
Therefore, the average speed of the truck is 45 km/hr.
Revision Table: Speed, Distance, Time Concepts
| Concept | Definition | Formula | Units (Common) |
|---|---|---|---|
| Speed | Rate at which an object covers distance. | \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\) | m/s, km/hr, mph |
| Distance | Total path covered by an object. | \(\text{Distance} = \text{Speed} \times \text{Time}\) | meters, kilometers, miles |
| Time | Duration for which motion occurs. | \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\) | seconds, minutes, hours |
| Average Speed | Total distance divided by total time. | \(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\) | m/s, km/hr, mph |
Additional Information on Average Speed
It's important to distinguish between average speed and average velocity. While average speed is the total distance covered divided by total time, average velocity is the total displacement divided by total time.
In this problem, since the truck is moving in a straight line and we are considering the total distance, the calculation using total distance divided by total time gives the average speed.
If the truck had traveled 40 km east in the first hour and then 40 km west in the second hour, the total distance would be 80 km (40 + 40), total time would be 2 hours, and average speed would be 40 km/hr. However, the displacement would be 0 km (since it returned to the starting point), and the average velocity would be 0 km/hr.
In problems involving varying speeds over different time intervals or distances, always use the total distance and total time to find the average speed.
Important Questions from Speed Time and Distance
A train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is
Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.
Rohit and Dinesh are 64 km apart. Rohit can walk at a speed of 15 km/hr and Dinesh at the speed of 17 km/hr. In how many hours will they meet if they are travelling towards each other?
Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
A worker covers a distance of 81 km in 11 hours. He travels partly on foot at 4.5 km/h and partly on bicycle at 15 km/h. What is the distance covered on the cycle?
