# If one walks inside a train in the same direction the train is moving, does one move faster than the train?

If one walks inside a train in the same direction the train is moving, does one move faster than the train? To answer this question, we need to presume a relative point of view, since speed is a relative quantity. Let us assume the point of view of someone standing outside the train, observing the motion of the train, and your movement inside the train. Now, in this case, if you are walking inside the train in the same direction in which the train is moving, then yes, that means that you are moving faster than the train is moving. It is because your speed of motion has been added to the rate at which the train is moving. If, however, you walk inside the train in the opposite direction to which the train is moving, then to the outside observer, your rate will be less than the speed of the train. It is because when you walk in a direction opposite to the train, your speed is subtracted from the speed of that train.

We can understand this with the help of an example. Let us say the train you are on is moving in the forward direction with a speed of 50 miles per hour. Firstly, let us assume that you are walking with a rate of 4 mph in the forward direction inside the train. Now to someone standing outside the train, your total speed is the speed of the train combined with your speed of walking, which is given as 50 + 4 = 54 mph. That means you are moving at a higher speed than the train. But let us say you walk with the same speed on the same train in the opposite direction. What will your total speed be then? It will be equal to the speed of the train minus your speed since you and the train are moving in opposite directions. Thus, it will be 50 – 4 = 46 mph, which is less than the speed of the train.

As we said above, speed is a relative quantity. That means that speed is always calculated with reference to some other object, which might be moving or stationary. If two friends John and George are sitting next to each other on a train moving at 52 mph, then they are both at rest relative to each other, i.e., their speed is zero with respect to each other. Yet if a person standing outside the train sees a train move past him/her, carrying John and George, then from this person’s frame of reference the train, John and George are all moving at the same rate, i.e., 52 mph. If George gets up and starts walking to the front of the train at the speed of 3 mph, then he has a total speed of 3 mph with respect to John, while John has 0 mph speed with respect to George. In other words, John is at rest. But from the point of view of an observer standing outside the train, John is moving at the same speed as the train, i.e., 52 mph, and George is moving at the rate of 52 + 3 = 55 mph, that is the speed of the train plus his walking speed.

In outer space, the Earth is moving too. For an astronaut in a spaceship that is stationary with respect to the Earth, it would seem as if the train moving on Earth, in the same direction as the Earth’s, is faster than the speed of the Earth. And if you are walking from the back of the train to the front, you are traveling faster than the train, which itself is moving faster than the Earth. It means that you are walking faster than both the Earth and the train. On top of that, if a fly were to walk across your cheek from your ear to your nose, it is traveling faster than you, and by extension, the train and the Earth!

So, to conclude, walking in a moving train in the same direction as the train’s movement makes the speed of your movement faster than that of the train.