Question

Two trains pass each other on parallel lines Each train is $100 \mathrm{~m}$ long. When they are going in the same direction the faster one takes 60 seconds to pass the other completely. If they are going in opposite directions, they pass each other completely in 10 seconds. Find the speed of the slower train in $\mathrm{km} / \mathrm{hr}$:
A) 30 km/hr
B) 42 km/hr
C) 48 km/hr
D) 60 km/hr

Answer 1

Hint:
The formula for speed is speed = distance divided by time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres $(\mathrm{m})$ and time is in seconds $(\mathrm{s}),$ so the units will be in metres per second $(\mathrm{m} / \mathrm{s})$. Calculate speed, distance or time using the formula $\mathrm{d}=\mathrm{st},$ distance equals speed times time. We can use the equivalent formula $\mathrm{d}=$ rt which means distance equals rate times time. distance = rate x time. To solve for speed or rate use the formula for speed, $\mathrm{s}=\mathrm{d} / \mathrm{t}$ which means speed equals distance divided by time.
Speed is a measure of how quickly an object moves from one place to another. It is equal to the distance travelled divided by the time. It is possible to find any of these three values using the other two. To find the speed, distance is over time in the triangle, so speed is distance divided by time.

Complete step by step solution:
Speed is the rate of change of distance with time. Acceleration is the rate of change of velocity with time. Velocity and acceleration are vector quantities, while speed is a scalar quantity.
Let the speed of the faster train be $\mathrm{x} \mathrm{km} / \mathrm{hr}$ and that of the slower train be y $\mathrm{km} / \mathrm{hr}$. Relative speed when both move in same direction $=(\mathrm{x}-\mathrm{y}) \mathrm{km} / \mathrm{hr}$
Relative speed when both move in opposite direction $=(\mathrm{x}+\mathrm{y})$
$\mathrm{km} / \mathrm{hr}$ Total distance travelled $=$ Sum of lengths of both the train
$=200 \mathrm{~m}$
Given, $\dfrac{200}{(\mathrm{x}-\mathrm{y}) \times \dfrac{5}{18}}=60$ and $\dfrac{200}{(\mathrm{x}-\mathrm{y}) \times \dfrac{5}{18}}=10$
$\Rightarrow \dfrac{3600}{5(\mathrm{x}-\mathrm{y})}=60$ and $\dfrac{3600}{5(\mathrm{x}+\mathrm{y})}=10$
$\Rightarrow \mathrm{x}-\mathrm{y}=\dfrac{3600}{300}=12 \ldots$ (i)
and $\mathrm{x}+\mathrm{y}=\dfrac{3600}{50}=72$.... (ii)
Adding eqn (i) and eqn (ii), we get $2 \mathrm{x}=84$
$\Rightarrow \mathrm{x}=42 \mathrm{~km} / \mathrm{hr}$
$\therefore$ From $(\mathrm{i}), \mathrm{y}=30 \mathrm{~km} / \mathrm{hr}$

Hence, the correct answer is option A.

Note:
Speed, being a scalar quantity, is the rate at which an object covers distance. On the other hand, velocity is a vector quantity; it is direction-aware. Velocity is the rate at which the position changes. The average velocity is the displacement or position change (a vector quantity) per time ratio. Speed has the dimensions of distance divided by time. The SI unit of speed is the metre per second, but the most common unit of speed in everyday usage is the kilometre per hour or, in the US and the UK, miles per hour.
In particular, if the speed is increasing, then the graph of the distance traveled by the car (as measured by the odometer) will bend upwards, becoming steeper and steeper. The most common formula for average speed is distance traveled divided by time taken. The other formula, if you have the initial and final speed, add the two together, and divide by 2.