Question

Two trains travel in opposite directions at 36 km/hr and 45 km/hr respectively. A man sitting in the slower train passes the faster train in 8 s. What will be the length of the faster train?
A. 80 m
B. 120 m
C. 150 m
D. 180 m

Answer 1

Hint: Approach to the problem is in such a way that First we will calculate their relative speed of the slower train with respect to the faster train by adding up the speeds of both the trains since they are travelling in opposite directions. Now, we know that the person sitting in the slower train must have travelled the distance equivalent to the length of the faster train and we are also given the time he spend on doing so which is 8 s and by that we will calculate the length of the train using the formula, $speed = \dfrac{{dis\tan ce}}{{time}}$.

Complete step-by-step answer:

Let the length of the faster train be X.

Let the slower train be A and the faster train be B and their speeds be Speed A and Speed B respectively.

Now, we know that Relative Speed = Speed A + Speed B because the trains are travelling in opposite directions.

We know that Speed A = 36 km/hr and Speed B = 45 km/hr

Relative Speed = 36 km/hr + 45 km/hr = 81 km/hr

Now we will convert the units into the S.I units i.e. m/s or meter per second .

We know that 1km = 1000m

We also know that 1hr = 60min and 1min = 60s
So, 1hr = 3600s

Now, $\left( {81} \right)km/hr = \left( {\dfrac{{81 \times 1000}}{{3600}}} \right)m/s = \left( {\dfrac{{45}}{2}} \right)m/\operatorname{s} $

We know that, $dis\tan ce = speed \times time$ ,where distance refers to the length of the train B i.e. faster train, Speed represents the relative speed which we just calculated and time refers to the time taken by the man sitting in the train A i.e. slower train to pass the train B i.e. faster train.
So, $X = \left( {\left( {\dfrac{{45}}{2}} \right)m/s} \right) \times 8s$
$X = 180m$

Hence, X = 180m which is the required length of the faster train which is the train travelling with 45 km/hr

Note: For such types of questions, just keep in mind what we meant by saying the relative speed i.e. relative speed is defined as the speed of a moving object with respect to another. When two objects move in the same direction, relative speed is calculated as their difference and when they move in opposite directions, relative speed is computed by adding the two speeds. Also, keep in mind that distance covered by any object is the product of the speed of the object and the time taken by the object in covering that distance.