Question

How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?

Answer 1

Answer:

55

Step-by-step explanation:

Formula: Distance = Speed x Time

Total distance = 165 + 660 = 825 m

Speed = 54 km/h = 54 * (5/18)  m/s

                             = 15  m/s

Time = 825 / 15 = 55 s

Answer 2

Answer:

A train 165 meters long running at the rate of 54 kmph will cross a bridge of length 660 in 55 seconds .

Step-by-step explanation:

• Speed of an object is defined as the rate of change of distance with respect to time. In other words, it is the ratio of distance covered by the object in a given interval of time.

$speed \: = \frac{distance}{time}$

• S.I. unit of speed is meter/sec.
• 1 kilometer (km) = 1000 meters (m)
• 1 hour = 60 minutes
• 1 minute = 60 seconds
• This gives 1 hour= 60 x 60 seconds.
• Converting 1km/hrs into meters/sec

$1 \: km/hrs \: = \frac{1000 \: meters}{60 \times 60 \: seconds} \\ = \frac{1000}{3600} = \frac{10}{36} \\ = \frac{5}{18} \: m/sec$

• 1km/hrs = 5/18 m/sec.

Given that :

• Length of train = 165 meters
• Length of bridge = 660 meters
• Total length of train and bridge combined = ( 165 + 660 )m = 825 meters.
• Speed of train = 54 km/hrs.
• Converting 54 km/hrs into meter/seconds using above relation, we get:

$54 \: km/hrs = \frac{5}{18} \times 54 meters/sec \\ = 5 \times 3 = 15 \: m/sec$

• Speed of train in m/sec = 15 m/sec.
• Time taken by train to completely cross the bridge is:

$time \: = \frac{distance}{speed} \\ = \frac{850}{15} \: sec \\ = 55 \: sec$

• Hence total time taken to cross the bridge is 55 sec.