Question

Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is
(a) 30 km/hr
(b) 45 km/hr
(c) 60 km/hr
(d) 75 km/hr

Answer 1

HINT: In these questions, the most important formula that would be used to get to the solution is as follows
The relation between distance, speed and time is as follows
\[distance=speed\times time\]

Complete step-by-step answer:

In this question, as it is mentioned that the two trains are moving in the opposite direction, then we can say that the net speed of the motion of the two trains taken together or taken to be a single system, is (x+ y).

(where x is the speed of first train and y is the speed of the second train)

As mentioned in the question, we have to find the speeds of the two trains by using the information that is provided in the question.

Now, as mentioned in the hint, the net speed of the motion is as follows

Speed=(x+ y)

(Where x is the speed of first train and y is the speed of the second train)

Now, as it is mentioned in the question that the speed of one train is twice the speed of the other, so, we can write as follows

y=2x

(Where x is the speed of first train and y is the speed of the second train)

Now, for crossing each other the total distance that is to be travelled by the system of the two trains is the entire length of the two trains which is (100+100)m=200m

Now, using the formula that is given in the hint, we can write as follows

\[\begin{align}

  & 200=(x+y)\times 8 \\

 & \dfrac{200}{8}=x+2x=3x \\

 & x=\dfrac{25}{3}m/\sec \\

\end{align}\]

(Using the information provided in the hint and mentioned above as well)

Now, for converting the speed into km/hr, we can do the following

\[\begin{align}

  & x=\dfrac{25}{3}m/\sec \\

 & x=\dfrac{25}{3}\times \dfrac{60\times 60}{1000}=\dfrac{25}{3}\times \dfrac{18}{5}=30km/hr \\

\end{align}\]


Now, hence, we can write the speed of the two trains as 30 km/hr and 60 km/hr.
So, the correct answer is (c).

NOTE: The students can make an error if they don’t know about the formula that is mentioned in the hint as follows
The relation between distance, speed and time is as follows
\[distance=speed\times time\]

Also, the students can make a mistake if they don’t know how to convert speed from m/sec to km/hr.