Question: A train leaves from a station and moves at a certain speed. After 2 hours, from the same station ano...

Question

A train leaves from a station and moves at a certain speed. After 2 hours, from the same station another train leaves and moves in the same direction at a speed of 60 mph. If it catches up the first train in 4 hours, then find the speed of the first train? Choose the correct answer.
(A) 40 mph
(B) 70 mph
(C) 90 mph
(D) 50 mph

Answer 1

Solution

As given in the question there are two trains leaving from the same station. Second train leaves the station 2 hours late as compared to the first one. Here we use the concept of relative speed, as the second train catches the first train in 4 hours, so the distance covered by both trains is the same. By formula we calculate the speed of the first train. The formula is $Dis\tan ce = Speed \times Time$ . We put the values in the formula and find the speed.

Complete step-by-step answer:
According to the question, Let A be the train which leaves the station first and S be the speed of the first train in mph.
After 2 hours the second train leaves the station, let us denote it as B and moves in the same direction whose speed is 60 mph.
Now the B train catches up with A in 4hours.
Let D be the common distance that both trains travel before they meet.
Hence Train A travel distance D in 6 hours i.e. 4+2 with speed S = $S \times 6$
Train B travels distance D in 4 hours = $60 \times 4$
Here we use the relative speed as both trains are in motion
Now we find the speed
$\therefore$ Distance covered by train A = Distance covered by train B
Now we put the values in the relation we get
$\Rightarrow S \times 6 = 60 \times 4$
$\Rightarrow S = \dfrac{{60 \times 4}}{6}$
$\Rightarrow S = \dfrac{{240}}{6}$
$\Rightarrow S = 40$
So the speed of the first train is 40 mph

So, the correct answer is “Option A”.

Note: In this question as the distance covered by both the trains is the same. So whenever there is a question where distance is the same we have to equate them and then find the speed. And we should also remember that we should check the units as well if they are not the same first we should make them equal and then calculate the speed.