Question

Two trains, 250 meters and 150 meters long respectively, are running on parallel lines. If they are running in the same directions, the faster train crosses the slower train in 40 seconds. If they are moving in the opposite direction they pass each other in eight seconds. What is the speed of the slower train?

Answer 1

The speed of the slower train: 20 m/s or 72 km/h

Explanation:

• Let the speed of the faster train be F m/s and that of the slower train S m/s

• When the trains are moving in the same direction the relative speed of the faster train with respect to the slower train is F - S m/s

• For the faster train to cross the slower train it has to cross the length of the slower train plus its own length

• The lengths of the two trains are 150 and 250 so the total distance to cross is 150 + 250 = 400 meters

• We are given that the time to traverse this distance of 400 meters = 40 seconds

• So relative speed, F - S = 400/40 seconds = 10 meters/second

• When the trains are traveling in opposite directions, the relative speed is F + S m/s
  

• The total distance traveled before the trains cross each other is the same: 150 + 250 = 400 meters

• We are given, that traveling in opposite directions it takes 8 seconds to cross each other
  
• Therefore relative speed F + S = 400 m / 8 m/s = 50 m/s

• We now have two equations relating F and S
  F - S = 10 (1)
  F + S = 50 (2)

• Subtract (2) from (1)
  (1) - (2) gives:
  
  F + S - (F - S) = 50 - 40
  F + S - F -(-S) = 40
  S + S = 40
  2S = 40/2 = 20

==> S = 20 m/s

This is the speed of the slower train

Answer 2

Explanation:

Let's call the length of the slower train L1 and the length of the faster train L2. Then, we have:

L1 = 150 meters

L2 = 250 meters

Let's also call the speed of the slower train S1 and the speed of the faster train S2. We are trying to find the value of S1.

When the trains are moving in the same direction, the faster train is "catching up" to the slower train, so the relative speed between them is the difference between their speeds:

relative speed = S2 - S1

The faster train needs 40 seconds to cross the slower train, which means that it covers the total distance between the two trains (L1 + L2) in 40 seconds at the relative speed:

L1 + L2 = (S2 - S1) * 40

When the trains are moving in opposite directions, they are getting closer to each other, so the relative speed between them is the sum of their speeds:

relative speed = S1 + S2

The two trains pass each other in 8 seconds, which means that they cover the total distance between them (L1 + L2) in 8 seconds at the relative speed:

L1 + L2 = (S1 + S2) * 8

Now we have two equations with two unknowns (S1 and S2), which we can solve using algebra. First, we can rearrange the first equation to get S2 in terms of S1:

S2 = (L1 + L2 + S1 * 40) / 40

Then we can substitute this expression for S2 into the second equation and simplify:

L1 + L2 = (S1 + (L1 + L2 + S1 * 40) / 40) * 8

L1 + L2 = (S1 * 9 + (L1 + L2) / 5)

S1 = (5 * (L1 + L2)) / (9 * 8)

S1 = 13.89 m/s (approx)

Therefore, the speed of the slower train is approximately 13.89 meters per second.