Solving for Average Speed Over Equal Distances
To find the average speed when covering three equal distances at different speeds, we use the formula:
$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $
Setting Up the Problem
Let the distance for each part of the journey be '$d$'. The total distance is therefore '$3d$'.
The speeds for the three parts are:
- Speed 1 ($v_1$): $30\text{ km/h}$
- Speed 2 ($v_2$): $45\text{ km/h}$
- Speed 3 ($v_3$): $90\text{ km/h}$
Calculating Time for Each Segment
Time taken for each distance is calculated using $ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $.
- Time 1 ($t_1$) = $ \frac{d}{30} $ hours
- Time 2 ($t_2$) = $ \frac{d}{45} $ hours
- Time 3 ($t_3$) = $ \frac{d}{90} $ hours
Calculating Total Time
Total time ($T$) is the sum of the times for each segment:
$ T = t_1 + t_2 + t_3 = \frac{d}{30} + \frac{d}{45} + \frac{d}{90} $
To add these fractions, find a common denominator, which is 90:
$ T = \frac{3d}{90} + \frac{2d}{90} + \frac{d}{90} = \frac{3d + 2d + d}{90} = \frac{6d}{90} $
Simplifying the total time:
$ T = \frac{d}{15} \text{ hours} $
Calculating Average Speed
Now, apply the average speed formula using the total distance ($3d$) and total time ($ \frac{d}{15} $):
$ \text{Average Speed} = \frac{3d}{\frac{d}{15}} $
$ \text{Average Speed} = 3d \times \frac{15}{d} $
$ \text{Average Speed} = 3 \times 15 = 45 \text{ km/h} $
Conclusion
The average speed of the car for the entire journey is $45\text{ km/h}$.
Similar Questions
A stock portfolio consists of four stocks. Stock A represents 20% of the portfolio and has a return of 6%. Stock B represents 30% of the portfolio and has a return of 8%. Stock C represents 20% of the portfolio and has a return of 4%. Stock D represents the remaining 30% of the portfolio and has a negative return of 5%. What is the average return of the portfolio?
- Ramesh walks at 5 km/h for 6 km and 6 km/h for 8 km. What is his average speed?
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- A train covers 3 equal distances at speeds in the ratio 4:5:6. What is the ratio of the average speed over the entire journey to the lowest speed?
- A train travels the first $100\text{ km}$ at $50\text{ km/h}$ and the next $100\text{ km}$ at $25\text{ km/h}$. What is the average speed for the total journey?
- An athlete runs a 300-meter race in 24 seconds. How much is his speed in km/h?
A car covers 40% of a certain distance at a pace of 20 km/h and the remaining distance at a pace of 30 km/h. What is the average speed of the car for the entire journey?
Dhiraj goes to his school from his house at a speed of 3.8 km/hr and returns at 2.6 km/hr. If he takes 5 hours going and coming, the distance between his house and school is:
Sachin covers half of his journey at 12 km/h and the remaining half at 3 km/h. His average speed is:
A man covered a certain distance in 3 parts with average speeds of 30 km/h, 60 km/h, and 90 km/h. What is his average speed over the entire journey, assuming equal distances?
Important Questions from Average Speed
A person covers a certain distance at the speed of 60 kmph and returns to the starting point at a speed of 40 kmph . Find the average speed (in km/hour) of the person for the whole journey.
A train runs at a speed of 28 kmph for 4 hours and 30 kmph for 5 hours and the remaining 40 kms in one hour. What is the average speed per hour?
Kapil travels for 4.5 hours at a speed of 50 km / h and 7.5 hours at a speed of 70 km / h. At the end of it, he finds that he covered only 6/7 of the total distance. At what average speed should he travel so that the remaining distance traveled in 5 hours?
An express train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long it take to reach its destination 600 km from the starting point?
A car has to cover 125 kms in 5 hours. What will be the average speed of the car if it has covered 90 kms in the first 3 hours?
