Question

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

a. 45 m
b. 50 m
c. 54 m
d. 72 m

Answer 1

To find the length of the train, we first calculate the relative speed between the train and the two persons. Then, we use the formula Length of train = (Relative speed x Time) to find the length of the train. Taking the positive value, we get the length of the train as 20 kilometers or 20000 meters.

Step-by-step explanation:

To find the length of the train, we need to first calculate the relative speed between the train and the two persons. We know that the train overtakes the first person in 9 seconds and the second person in 10 seconds.

Let's calculate the relative speeds:

Relative speed with the first person = (Speed of train - Speed of person) = (2 kmph - 4 kmph) = -2 kmph

Relative speed with the second person = (Speed of train - Speed of person) = (4 kmph - 2 kmph) = 2 kmph

-2 kmph and 2 kmph are the relative speeds of the train with respect to the first and second person respectively.

Now, we can use the formula: Length of train = (Relative speed x Time)

Length of train = (-2 kmph x 9s) = -18 km

The length of the train is negative, which is not possible. So, we need to take the positive value.

Length of train = (2 kmph x 10s) = 20 km

Since the speed and time are given in kmph and seconds respectively, we need to convert the length of the train to meters. 1 km = 1000 m. So, Length of train = 20 km x 1000 m/km = 20000 m.

Therefore, the length of the train is 20000 meters or 20 kilometers.