Average Speed Calculation for Train Journey
Problem Details
- Distance for the first part ($d_1$): $100\text{ km}$
- Speed during the first part ($v_1$): $50\text{ km/h}$
- Distance for the second part ($d_2$): $100\text{ km}$
- Speed during the second part ($v_2$): $25\text{ km/h}$
- Objective: Find the average speed ($v_{avg}$) for the total journey.
Solution Steps
-
Calculate the time taken ($t_1$) for the first $100\text{ km}$.
Using the formula: Time = Distance / Speed
$t_1 = \frac{d_1}{v_1} = \frac{100\text{ km}}{50\text{ km/h}} = 2\text{ hours}$
-
Calculate the time taken ($t_2$) for the next $100\text{ km}$.
Using the formula: Time = Distance / Speed
$t_2 = \frac{d_2}{v_2} = \frac{100\text{ km}}{25\text{ km/h}} = 4\text{ hours}$
-
Determine the total distance and total time.
Total Distance ($d_{total}$): $d_{total} = d_1 + d_2 = 100\text{ km} + 100\text{ km} = 200\text{ km}$
Total Time ($t_{total}$): $t_{total} = t_1 + t_2 = 2\text{ hours} + 4\text{ hours} = 6\text{ hours}$
-
Calculate the average speed ($v_{avg}$) for the total journey.
Formula: Average Speed = Total Distance / Total Time
$v_{avg} = \frac{d_{total}}{t_{total}} = \frac{200\text{ km}}{6\text{ hours}}$
$v_{avg} = \frac{100}{3}\text{ km/h}$
$v_{avg} \approx 33.33\text{ km/h}$
Result
The average speed for the total journey is approximately $33.33\text{ km/h}$.
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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?
