Introduction / Context:
In many aptitude and competitive exams, problems involving speed, distance and time are very common. This question asks you to determine how many seconds a train, moving with a uniform speed of 72 km/h, will take to cover a distance of 1400 m. To solve such questions correctly and quickly, you must be comfortable with unit conversions (especially km/h to m/s) and with the basic relationship between speed, distance and time.
Given Data / Assumptions:
- The speed of the train is 72 km/h.
- The distance to be covered is 1400 m.
- The train moves at a constant (uniform) speed.
- We assume there are no stops or changes in speed during the motion.
Concept / Approach:
The fundamental formula relating speed, distance and time is:
speed = distance / time
From this, time can be written as:
time = distance / speed
However, the distance is given in metres (m) and the speed is given in kilometres per hour (km/h). To apply the formula consistently, we must convert the speed to metres per second (m/s). The standard relation is:
1 km/h = (1000 / 3600) m/s = 5 / 18 m/s
Step-by-Step Solution:
Step 1: Convert the speed from km/h to m/s.
Speed in m/s = 72 * (5 / 18).
72 / 18 = 4, so speed = 4 * 5 = 20 m/s.
Step 2: Use the time formula time = distance / speed.
Distance = 1400 m, speed = 20 m/s.
Time = 1400 / 20 seconds.
1400 / 20 = 70 seconds.
Therefore, the train takes 70 seconds to cover 1400 m.
Verification / Alternative check:
We can perform a quick reasonableness check. At 20 m/s, the train covers 20 m every second. In 70 seconds, it will cover:
distance = speed * time = 20 * 70 = 1400 m
This matches the required distance exactly, so the calculation is consistent and correct.
Why Other Options Are Wrong:
70 seconds is correct, so the other values are incorrect for the given data.
60 seconds would correspond to a speed of 1400 / 60 ≈ 23.33 m/s, which is more than 20 m/s.
72 seconds would mean a lower speed of about 19.44 m/s, not 20 m/s.
80 seconds or 84 seconds would correspond to even smaller speeds and do not match a constant speed of 72 km/h.
Common Pitfalls:
A common mistake is to directly substitute speed = 72 into the formula without converting to m/s, mixing kilometres, metres, hours and seconds incorrectly. Another frequent error is to misapply the km/h to m/s conversion factor, for example using 18 / 5 instead of 5 / 18. Students also sometimes invert the formula and compute speed = time / distance instead of time = distance / speed. Carefully keeping track of units and the correct formula avoids these issues.
Final Answer:
The train takes
70 seconds to cover a distance of 1400 m at a speed of 72 km/h.
Discussion & Comments