Understanding the Train and Tunnel Problem
This problem asks us to calculate the speed of a goods train based on its length, the length of a tunnel it passes through, and the time taken.
Calculating Total Distance Covered
For a train to completely pass through a tunnel, the total distance it needs to cover is the sum of its own length and the length of the tunnel. This is because the train starts covering the tunnel distance from the moment its front enters, and finishes when its rear end exits the tunnel.
- Length of the goods train = 350 m
- Length of the tunnel = 1250 m
Let $D$ represent the total distance covered. The calculation is:
$$ D = \text{Length of train} + \text{Length of tunnel} $$
Substituting the given values:
$$ D = 350 \, \text{m} + 1250 \, \text{m} $$
$$ D = 1600 \, \text{m} $$
Determining Train Speed in Meters per Second (m/s)
Speed is defined as distance traveled per unit of time. We can use the formula:
$$ \text{Speed} = \frac{\text{Total Distance}}{\text{Time taken}} $$
We have:
- Total Distance ($D$) = 1600 m
- Time taken ($t$) = 80 seconds
Let $S$ be the speed in m/s. The calculation is:
$$ S = \frac{D}{t} $$
$$ S = \frac{1600 \, \text{m}}{80 \, \text{s}} $$
$$ S = 20 \, \text{m/s} $$
Converting Speed from m/s to Kilometers per Hour (km/h)
The options provided are in kilometers per hour (km/h). To convert speed from meters per second (m/s) to kilometers per hour (km/h), we multiply by the conversion factor $\frac{18}{5}$.
$$ \text{Speed in km/h} = \text{Speed in m/s} \times \frac{18}{5} $$
Using the speed calculated in m/s:
$$ \text{Speed in km/h} = 20 \times \frac{18}{5} $$
First, divide 20 by 5:
$$ \text{Speed in km/h} = 4 \times 18 $$
Now, perform the multiplication:
$$ \text{Speed in km/h} = 72 \, \text{km/h} $$
Final Answer Derivation
The calculation shows that the speed of the goods train is 72 km/h. This is derived by first finding the total distance the train travels (its own length plus the tunnel's length) and then dividing this distance by the time taken. Finally, the speed is converted from meters per second to kilometers per hour.
Similar Questions
- Ram, standing on a railway platform, noticed that a train took 36 seconds to completely pass through the platform, which was 108 m long, and it took 12 seconds in passing him. Find the speed of the train.
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- Two trains of equal length take 10 s and 20 s, respectively, to cross a pole. If these trains are moving in the same direction, then how long will they take to cross each other?
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- A train crosses a 1000 m long bridge in 52 seconds and another 700 m long bridge in 40 seconds. Assuming the train is running at a uniform speed, what is the speed (in km/h) of the train?
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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:
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:
The length of a train and that of a platform are equal. If with a speed of 108 km/hr the train crosses the platform in one minute. Then the length of the train (in metres) is:
