Speed of the train is 63 Km/hr, then speed per second
=> 63 $\displaystyle \times \frac{5}{18}$ = 17.5 meters/sec.
Speed of the train per second is 22.5 meters/sec.
Speed of the train per hour => 22.5 $\displaystyle \times \frac{18}{5}$ = 81 km/hr.
Time taken by a train to cross a pole = Time taken to cross its own length.
Length of the train = 54 $\displaystyle \times \frac{5}{18} \times 15$ = 225 meters.
Rule: While crossing a platform a train covers the length of the platform and its own length.
Distance covered by the train in 30 seconds, moving at 72 Km/hr is 72 $\displaystyle \times \frac{5}{18} \times 30$ = 600 meters.
Length of the train = Distance covered – length of the platform = 600 m – 250 m = 350 meters.
Rule: While crossing a bridge a train covers the length of bridge and its own length.
Distance covered by the train in 45 seconds at 60 Km/hr
=> 60 $\displaystyle \times \frac{5}{18} \times 45$ = 750 meters.
Length of the trains = $\displaystyle \frac{750}{2}$ = 375 meters [ as both length of the train and bridge is equal ]
Speed per second = $\displaystyle \frac{\text{Length of the train} + \text{Length of the platform}}{\text{Time}}$
Speed per second = $\displaystyle \frac{200 \ \text{m} \ + \ 250 \ \text{m}}{20 \ \text{sec}} \ = \ \frac{450}{20}$ = 22.5 meters/sec.
Speed of the train per hour = 22.5 $\displaystyle \times \frac{18}{5}$ = 81 km/hr.
While crossing a platform a train covers the length of the platform and its own length.
Time taken to cross the platform | = |
30 seconds |
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(-)Time taken to cross the signal pole | = |
10 seconds [train length] |
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To cross only platform length | = |
20 seconds |
Ratio of time taken to cross plat form to train = 20 sec : 10 sec or 2 : 1
Distance covered in 24 seconds = length of the train + length of the platform.
Speed of the train per second => $\displaystyle \frac{200 + 400}{24} = \frac{600}{24}$ = 25 m/s.
Speed of the train = 25 $\displaystyle \times \frac{18}{5}$ = 90 km/hr.
Time taken to cross a bridge of 800 meters => $\displaystyle \frac{\text{bridge length} + \text{train length}}{\text{speed}}$
Time taken to cross the bridge => $\displaystyle \frac{800 \ \text{m} \ + 200 \ \text{m}}{25 \ \text{m/s}} = \frac{1000}{25}$ = 40 seconds.
As the speed of the train is 1 Km/min, and length of the train is 1 Km.
Length of the tunnel = 1 Km, distance to be covered = 1 + 1 = 2 Km.
Therefore the train takes 2 min to pass through the tunnel.
Time taken = 4 Hrs [From 7:00 am to 11:00 am].
If speed increases by R% then time reduces by = $\displaystyle \frac{\text{R}}{100 + \text{R}} \times 100$
Then time reduces by = $\displaystyle \frac{25}{125} \times 100$ = 20%.
4 hours = 240 minutes = 20% of 240 = 48 minutes.
4 hours – 48 minutes = 3 hours and 12 minutes.
The train reaches at 12:00 Noon + 3 hrs 12 min = 3:12 PM.
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If a train is moving at A km/h then its speed per second is
A $\displaystyle \times \frac{5}{18}$ meters second.
If a train is moving at B meters per second then its speed per hour is
B $\displaystyle \times \frac{18}{5}$ km/hour.
Time taken to cross pole/tree/standing person etc.. is time taken to cross its own length of the train.
While crossing a platform/Bridge/Tunnel the train covers the length of the platform/Bridge/Tunnel and its own length.
If two trains are moving at x km/hr and y km/hr respectively, then relative speed if they are moving in.
Opposite direction = [ x + y ] km/hr
Same direction = [ x – y ] km/hr
Note: Add lengths of the trains in both the cases.
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