A man covered a distance of 18 km in 3 hours, 7.2 km in 2 hours and 15 km in 5 hours. What is the average distance traveled by him per hour?
4.02 km
Calculating Average Distance Per Hour
The problem asks us to find the average distance covered by a man per hour. This is essentially asking for the average speed of the man over the entire journey.
To find the average speed, we need two things:
- The total distance traveled.
- The total time taken for the journey.
The average speed is then calculated by dividing the total distance by the total time.
Steps to Calculate Average Distance
Let's break down the journey into the given segments and sum up the distance and time for each part.
| Segment | Distance (km) | Time (hours) |
|---|---|---|
| 1 | 18 | 3 |
| 2 | 7.2 | 2 |
| 3 | 15 | 5 |
1. Calculate Total Distance
Add the distances covered in each segment:
\(\text{Total Distance} = 18 \text{ km} + 7.2 \text{ km} + 15 \text{ km}\)
\(\text{Total Distance} = 40.2 \text{ km}\)
2. Calculate Total Time
Add the time taken for each segment:
\(\text{Total Time} = 3 \text{ hours} + 2 \text{ hours} + 5 \text{ hours}\)
\(\text{Total Time} = 10 \text{ hours}\)
3. Calculate Average Distance per Hour (Average Speed)
Divide the total distance by the total time:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
\(\text{Average Speed} = \frac{40.2 \text{ km}}{10 \text{ hours}}\)
\(\text{Average Speed} = 4.02 \text{ km/hour}\)
So, the average distance traveled by the man per hour is 4.02 km.
Comparing this result with the given options, we find that 4.02 km matches one of the choices.
Revision Table: Key Formulas for Average Speed
| Concept | Formula |
|---|---|
| Average Speed | \(\frac{\text{Total Distance}}{\text{Total Time}}\) |
| Total Distance (multiple segments) | Sum of distances of all segments |
| Total Time (multiple segments) | Sum of time taken for all segments |
Additional Information on Average Speed Calculations
The calculation of average speed is a fundamental concept in distance, speed, and time problems. It's important to remember that average speed is not simply the average of the speeds in different segments unless the time taken for each segment is the same.
- If an object travels different distances in the same amount of time, the average speed calculation is straightforward using the total distance and total time.
- If an object travels at different speeds for the same duration of time, the average speed is the simple average of the speeds.
- If an object travels at different speeds over different distances (or for different times, as in this problem), you must calculate the total distance and total time first before dividing to find the average speed.
Understanding the difference between calculating average speed based on distance and time versus just averaging different speeds is crucial for solving these types of problems correctly.
Important Questions from Boat and River
A boat sails 15 km of a river towards upstream in 5 hours. How long (in hours) will it take to cover the same distance downstream, if the speed of river is one-fourth the speed of the boat in still water?
The speed of boat upstream is 5 kmph. Its speed in still water is 10 kmph. How many minutes will it take to row 25 km downstream?
Sudha can travel a certain distance downstream in 6 hours by boat and return to the starting point in 9 hours. If the stream flows at a speed of 3 km/h, how long (in hours) will it take to cover a distance of 67.5 km in still water?
The downstream speed of a boat is 20 km/hr and the speed of stream is 4 km/hr. What will be the total time taken by the boat to cover 160 km downstream and 96 km upstream?
The ratio of the speeds of a boat in still water and the speed of the river is 3 ∶ 1. The boat takes 45 minutes for a round trip journey. Find the distance of the whole trip if the speed of the stream is 4 km/hr.
