Question

A train of 320m crosses a platform in 24 seconds at the speed of 120km/h. while a man crosses the same platform in 4 minutes. What is the speed of man in m/s?.
(a) 2.4
(b) 1.5
(c) 1.6
(d) 2.0

Answer 1

Hint: Firstly convert time for the train from seconds to hour and substitute its value in the speed-distance-time relation given as d = s t. Now convert the distance we get from km to m as we need to find the speed of man in m/s. apply the time taken by man in the formula to calculate the final answer.

Complete step-by-step answer:
We know the speed-distance-time relation is given as d = s t, where d is the distance travelled in km, s is the speed of the body in km/hr and t is the time taken in hours by the body to travel the signified distance (d).
The time taken t is in hours in the speed-distance-time relation so convert the time taken by the train to cross the platform to hours.
The conversion for seconds to hour is given by \[t\left( \text{in hour} \right)=\dfrac{t\left( \text{in seconds} \right)}{3600}\].
Applying the above conversion rule for time t we get,
\[t\left( \text{in hour} \right)=\dfrac{24}{3600}\]
Dividing 24 by 3600 we get time t as,
t(in hour) = 0.0067
Applying the speed-distance-time relation to find the distance travelled by the train at speed s = 120 km/h,
By substituting t = 0.0067 in the above mentioned formula we get,
\[d=120\left( 0.0067 \right)\]
On multiplying 120 by 0.0067 the distance travelled by the train in km is,
d = 0.804
The conversion for km to m is given by \[d\left( \text{in m} \right)=1000\cdot d\left( \text{in km} \right)\].
Applying the above conversion rule for distance d we get,
\[d\left( \text{in m} \right)=1000\cdot 0.804\]
On multiplying 1000 with 0.804 we get,
d (in m) = 804
For the train to cross the platform its length of 320m should be subtracted from the distance of the platform therefore we get the distance as,
d = 804 – 320
Subtracting 320 from 804 the exact distance of the platform is,
d = 484
Now we know the distance of the platform is the same for man and the train, therefore the man travels a distance d = 484m in time 4 minutes.
The conversion for minutes to seconds is given by \[t\left( \text{in seconds} \right)=60\cdot t\left( \text{in minutes} \right)\].
Applying the above conversion rule for time taken by the man to cross the platform we get,
\[y\left( \text{in seconds} \right)=60\cdot 4\]
Multiplying 60 by 4 we get time y as,
y (in seconds) = 240
We know the speed-distance-time relation is given as \[e=\dfrac{d}{y}\], where d is the distance travelled in m, e is the speed of the man in m/s and y is the time taken in seconds by the man to travel the signified distance (d).
Now find the speed e of man in m/s by using d = 804m and time taken y = 240 seconds in the above relation,
\[e=\dfrac{484}{240}\]
Dividing 484 by 240 we get speed e in m/s as,
e = 2.01
By approximating the value we get speed of man e = 2.0 m/s.
Hence option (d) is the correct answer.

Note: The possible error that you may encounter is the conversion of units. All the units should be the same before applying any operation on them. Carefully convert time from seconds to hours in the case of the train and the time for man should be converted to seconds. Similarly the distance travelled by the train must be subtracted from its length in order to find the distance of the platform for further calculation.