A train passes a platform, 225 m length, in 21 sec and a man, standing on the platform, in 6 sec. Find: (i) the length of the train. (ii) the speed of the train.
Answers
Answer:(i).ength of the train is 90 meters.(ii). speed of the train is 15 meters per second
Step-by-step explanation:
Let's assume that the length of the train is 'x' meters, and its speed is 'v' meters per second.
(i) To find the length of the train, we can use the formula:
Distance = Speed × Time
When the train passes the platform, it covers a distance equal to the sum of the length of the platform and the length of the train. Therefore,
225 + x = v × 21
Similarly, when the train passes the man, it covers a distance equal to the length of the train. Therefore,
x = v × 6
Now, we can solve these two equations simultaneously to find the values of 'x' and 'v'. We can start by dividing the second equation by 6:
x/6 = v
Substitute this value of 'v' in the first equation:
225 + x = 21(x/6)
Simplify and solve for 'x':
225 + x = 3.5x
2.5x = 225
x = 90
Therefore, the length of the train is 90 meters.
(ii) To find the speed of the train, we can use the value of 'x' that we just found and substitute it in either of the two equations that we used earlier. Let's use the second equation:
x = v × 6
Substitute x = 90:
90 = v × 6
v = 15
Therefore, the speed of the train is 15 meters per second, or 54 kilometers per hour (since 1 kilometer = 1000 meters and 1 hour = 3600 seconds, we can convert meters per second to kilometers per hour by multiplying by 3.6).