A. 100m
B. 150m
C. 200m
D. 300m
Answer
Correct Answer: D. 300m
Solution
Let’s start by converting the speed of the train from km/h to m/s, as the length of the train and the time taken to cross the bridge are given in meters and seconds respectively.
48 km/h = (48 x 1000) / 3600 m/s [1 km/h = 1000 m/h, 1 hour = 3600 seconds] = 13.33 m/s (rounded to two decimal places)
Now let’s use the formula:
distance = speed x time
Let “x” be the length of the bridge in meters. The distance the train covers to completely cross the bridge is the sum of the length of the train and the length of the bridge, i.e., 100 + x.
So we have:
distance = speed x time 100 + x = 13.33 x 30 [time taken is 30 seconds] 100 + x = 399.9 x = 399.9 – 100 x = 299.9
Therefore, the length of the bridge is 299.9 meters (rounded to one decimal place).
Reader Comments
At 48 km/h the train goes 48000 meters in one hour. That means that it travels 48000 meters in 3600 seconds; which is equal to 13 and 1/3 meters per second. With that speed, it takes 100 /13,333 seconds to go the whole length of the train; 100 meters. 100/13,333 is equal to 7,5 almost exactly. Then, divide 30 seconds with 7,5, and you get how many ‘train-lengths’ you travel in that sequence. 30 divided by 7,5 is exactly 4. Reduce 1 from 4 and you get 3. 3 train lengths is the length of the bridge, which is equal to 300 meters.
Convert 48 km/hr to m/s: → 40/3 m/s
In 30 seconds, the train would cover: (30) * (40/3) = 400 m
The length of the bridge plus the train length = 400 m
Then the bridge alone would be 400 – 100 = 300 m. (Answer).