A train passes two persons walking in the same direction in which the train is going. These persons are walking at the rates of 2 km/hr and 4 km/hr, respectively, and are completely crossed by the train in 9 seconds and 10 seconds, respectively. What is the length of the train?
50 meters
Let the speed of the train be \(v\) km/h and its length be \(L\) metres.
Since the persons walk in the same direction as the train, the relative speed with the first person is \((v - 2)\) km/h, and with the second person is \((v - 4)\) km/h.
Using \(L = (v-2) \times \frac{5}{18} \times 9\) and \(L = (v-4) \times \frac{5}{18} \times 10\), equate both: \((v-2) \times 9 = (v-4) \times 10\).
\(9v - 18 = 10v - 40 \Rightarrow v = 22\) km/h.
So \(L = (22-2) \times \frac{5}{18} \times 9 = 20 \times \frac{5}{18} \times 9 = 50\) metres.
Hence, the length of the train is 50 metres.
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 180 m long is running at a speed of 90 km/h. How long will it take to pass a post?
- A train service got disrupted due to an accident after a travel of 30 km. The speed was reduced to four-fifth of the original speed. This caused it a delay of 45 min. If the accident had happened 18 km farther, it would have been running late for 36 min. What was the original speed of the train?
- 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?
- 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 300-m-long train crosses an electric pole in 5 s. Find the speed of the train.
- Simplify the following. $\sqrt{2 + \sqrt{2 + 2\cos 4\theta}}$
- A train is moving at a uniform speed of 75 km/h. Find the time required by the train to cover a distance of 250 km.
- A train that is 110 m in length is running at 90 km/h. How much time will the train take to cross a bridge that is 180 m in length?
Important Questions from Problem on Trains
Eight railway stations A, B, C, D, E, F, G and H are connected either by two-way passages or one-way passages. One-way passages are from C to A, E to G, B to F, D to H, G to C, E to C and H to G. Two-way passages are between A and E, G and B, F and D, and E and D.
If the route between G and C is closed, which one of the following stations need not be passed through while travelling from H to C?
A daily train is to be introduced between station A and station B starting from each end at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the Shuttle Service?
A train with a uniform speed passes a 122 meters long platform in 17 seconds and a 210 meters long bridge in 25 seconds. The speed of the train is:
How long does a train 153 meters long running at the rate of 90 kmph take to cross a bridge 622 meters in length?
A train passes a 360 metre long platform in 40 seconds and a man standing on the platform in 16 seconds. The speed of the train is:
