Average Speed Calculation for Ramesh's Journey
To determine the average speed, we need to find the total distance covered and divide it by the total time taken for the journey.
The formula for average speed is:
$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $
Calculating Total Distance
Ramesh's journey consists of two parts:
- Distance 1: 6 km
- Distance 2: 8 km
Total distance = 6 km + 8 km = 14 km.
Calculating Total Time
Time is calculated using the formula: $ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $
- Time for the first part (T1): $ T_1 = \frac{6 \text{ km}}{5 \text{ km/h}} = 1.2 \text{ hours} $
- Time for the second part (T2): $ T_2 = \frac{8 \text{ km}}{6 \text{ km/h}} = \frac{4}{3} \text{ hours} $
Total time = $ T_1 + T_2 = 1.2 \text{ h} + \frac{4}{3} \text{ h} $
To add these, we find a common denominator:
Total time = $ \frac{6}{5} \text{ h} + \frac{4}{3} \text{ h} = \frac{(6 \times 3) + (4 \times 5)}{15} \text{ h} = \frac{18 + 20}{15} \text{ h} = \frac{38}{15} \text{ hours} $
Calculating Average Speed
Using the total distance and total time:
$ \text{Average Speed} = \frac{14 \text{ km}}{\frac{38}{15} \text{ hours}} $
$ \text{Average Speed} = 14 \times \frac{15}{38} \text{ km/h} $
$ \text{Average Speed} = \frac{210}{38} \text{ km/h} $
Simplifying the fraction:
$ \text{Average Speed} = \frac{105}{19} \text{ km/h} $
Converting to a decimal:
$ \text{Average Speed} \approx 5.53 \text{ km/h} $
Thus, Ramesh's average speed is approximately 5.53 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?
- A person walks 5 km to a destination in 1 hour. On the return journey, they walk the same 5 km distance back to the starting point in 50 minutes. What is the average speed of the person for the entire journey?
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- 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?
- A car covers three equal distances at speeds of $30\text{ km/h}$, $45\text{ km/h}$, and $90\text{ km/h}$, respectively. 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?
