Problem Analysis
We need to find the length of the train ($L$) given two scenarios:
- The train crosses a man (point object) in 10 seconds.
- The train crosses a platform of 260 m in 20 seconds.
Let the speed of the train be $S$ m/s.
Calculating Train Speed and Length
Scenario 1: Crossing a man
When a train crosses a man, the distance covered is equal to the length of the train ($L$).
Time = Distance / Speed
$10 = L / S$
From this, we get the relation: $L = 10S$ (Equation 1)
Scenario 2: Crossing a platform
When a train crosses a platform, the total distance covered is the length of the train ($L$) plus the length of the platform (260 m).
Time = Total Distance / Speed
$20 = (L + 260) / S$
This gives us: $20S = L + 260$ (Equation 2)
Solving for Length ($L$)
Substitute the value of $L$ from Equation 1 into Equation 2:
$20S = (10S) + 260$
Subtract $10S$ from both sides:
$20S - 10S = 260$
$10S = 260$
Calculate the speed $S$:
$S = 260 / 10$
$S = 26$ m/s
Now, substitute the speed $S$ back into Equation 1 to find the length $L$:
$L = 10S$
$L = 10 \times 26$
$L = 260$ m
Conclusion
The length of the train is 260 meters.
Similar Questions
- A train overtakes two persons walking along a railway track. The first one walks at 9 km/hr. The other one walks at 12.6 km/hr. The train needs 13.5 and 15 seconds, respectively, to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
- A train that is 220 m long overtakes a man moving at a speed of 10 km/hr (in same direction) in 44 seconds. How much time (in seconds) will it take this train to completely cross another train of a length of 315 m, moving in the opposite direction at a speed of 79 km/hr?
- A train 180 m long is running at a speed of 90 km/h. How long will it take to pass a post?
- A 300-m-long train crosses an electric pole in 5 s. Find the speed of the train.
- Find the time taken by a 450 m long train travelling at the speed of 80 km/h to cross a platform of length 150 m.
- Two trains start from stations A and B and travel towards each other at the speeds of 60 km/h and 70 km/h respectively. At the time of their meeting, the second train has travelled 100 km more than the first. The distance between A and B is:
- A train passes two bridges of lengths 600 m and 200 m in 80 s and 40 s respectively. The length of the train is:
- Two trains 136 m and 185 m in length respectively are running in opposite directions, one at a speed of 70 km/h and the other at a speed of 65 km/h. In what time will they be completely clear of each other from the moment they meet?
- Simplify the following. $\sqrt{2 + \sqrt{2 + 2\cos 4\theta}}$
- A train passes two persons who are walking in the opposite direction of the train at the rates of $4 \text{ m/s}$ and $10 \text{ m/s}$ in 10 seconds and 8 seconds respectively. What is the speed of the train?
Important Questions from Problem on Trains
A train is to cover 370 km at a uniform speed. After running 100 km, the train could run at a speed 5 km/h less than its normal speed due to some technical fault. The train got delayed by 36 minutes. What is the normal speed of the train, in km/h?
A train travelling at 36 km/h crosses a pole in 25 seconds. How much time (in seconds) will it take to cross a bridge 250 m long?
A train covers 450 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less to cover the same distance. How much time will it take to cover 315 km at its usual speed?
A train crosses a pole in 12 sec, and a bridge of length 170 m in 36 sec. Then the speed of the train is:
The ratio of the speeds of two trains is 2 : 7. If the first train runs 250 km in 5 hours, then the sum of the speeds (in km/h) of both the trains is:
