A train 125m long passes a man running at 5kmph in the same direction in which the train is going in 10 seconds. Find the speed of the train (in kmph).
Last updated date: 19th Mar 2023
•
Total views: 305.4k
•
Views today: 6.84k
Answer
305.4k+ views
Hint: Assume the speed of the train to be x kmph. Calculate the speed of the train relative to the man. As the man is a point object, we can consider that the train covers the distance equal to its length in the given time, which is 10 seconds. Solve the equation formed by relating speed of train with distance covered by train and time taken to travel the distance, to get the value of speed of train.
Complete step-by-step answer:
We have a 125m long train which passes a man running at a speed of 5kmph in the same direction in which the train is going in 10 seconds. We have to calculate the speed of the train.
Let’s assume that the speed of the train is x kmph.
So, the speed of the train relative to man will be \[x-5\] kmph.
Considering the man as a point object, we observe that the train covers a distance equal to its own length in 10 seconds. Thus, the train covers a distance of 125m in 10 seconds by running at a speed of \[x-5\] kmph.
We know that speed of an object is the ratio of distance covered by an object to the time taken by the object to cover that distance.
Thus, we have speed of the train \[=x-5kmph=\dfrac{125}{10}m/\sec =12.5m/\sec \].
We have to convert the speed of the train in \[m/\sec \] to kmph.
We know that \[1m/\sec =3.6kmph\].
To convert x \[m/\sec \] into kmph, we will multiply x by 3.6.
Thus, we have \[12.5m/\sec =12.5\times 3.6kmph=45kmph\].
So, we have \[x-5kmph=45kmph\].
\[\Rightarrow x=45+5=50kmph\]
Hence, the speed of the train is 50kmph.
Note: It’s very necessary to keep the units of speed, distance and time in mind. If we solve the question without keeping the units the same on both sides of the equation, we will get an incorrect answer. We can also solve the question by considering the speed of man relative to speed of train and then solving equations to get the speed of train.
Complete step-by-step answer:
We have a 125m long train which passes a man running at a speed of 5kmph in the same direction in which the train is going in 10 seconds. We have to calculate the speed of the train.
Let’s assume that the speed of the train is x kmph.
So, the speed of the train relative to man will be \[x-5\] kmph.
Considering the man as a point object, we observe that the train covers a distance equal to its own length in 10 seconds. Thus, the train covers a distance of 125m in 10 seconds by running at a speed of \[x-5\] kmph.
We know that speed of an object is the ratio of distance covered by an object to the time taken by the object to cover that distance.
Thus, we have speed of the train \[=x-5kmph=\dfrac{125}{10}m/\sec =12.5m/\sec \].
We have to convert the speed of the train in \[m/\sec \] to kmph.
We know that \[1m/\sec =3.6kmph\].
To convert x \[m/\sec \] into kmph, we will multiply x by 3.6.
Thus, we have \[12.5m/\sec =12.5\times 3.6kmph=45kmph\].
So, we have \[x-5kmph=45kmph\].
\[\Rightarrow x=45+5=50kmph\]
Hence, the speed of the train is 50kmph.
Note: It’s very necessary to keep the units of speed, distance and time in mind. If we solve the question without keeping the units the same on both sides of the equation, we will get an incorrect answer. We can also solve the question by considering the speed of man relative to speed of train and then solving equations to get the speed of train.
Recently Updated Pages
If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
