Question

A, B and C start from the same place and travel the same directions at speeds of \[30,\text{ }40\text{ }and\text{ }60\text{ }km/hr\]respectively. B starts two hours after A. If B and C overtake A at the same instant how many hours after A did C start?
A) \[3\]
B) \[3.5\]
C) \[4\]
D) \[4.5\]

Answer 1

Hint: In the given question, we have been asked a question that is related to relativity. This kind of question can be solved by using the concept of relative speed. When two bodies move in opposite directions, then the Relative Speed is equal to the Sum of Speeds and when two bodies move in the same direction then the Relative Speed is equal to the Difference of Speeds.

Complete step-by-step answer:
According to the question,
B starts when A already travelled for \[2hours\],
Distance travelled by A in 2 hours = \[speed\ of\ A\ per\ hour\times \ time\ taken\ \]= \[2\times 30km/hr\]= \[60km\]
When A covers the distance of \[60km\], B is still at the starting point.
When two bodies move in the same direction then the Relative Speed = Difference of Speeds= \[\left( 40-30 \right)km/hr\text{ }=\text{ }10km/hr~\]
Time taken by B to cover A with a relative speed of 10km/hr = \[\dfrac{dis\tan ce}{speed}\]= \[\dfrac{60}{10}=6hours\]
Therefore, B takes \[6hours\]to cover the distance of 60km and overtakes A.
So, B overtakes A in total of = \[2hours+6hours=8hours\]
Now,
Distance travelled by A in 8 hours = \[speed\ of\ A\ per\ hour\times \ time\ taken\ \]= \[30km/hr\times 8\]= \[240km\]
It is the point where C overtakes A.
Time taken by C to cover the distance of \[240km\] in = \[\dfrac{dis\tan ce\ travelled}{speed\ km/hour}=\dfrac{240}{60}=4hours\]
Therefore, C started after A in = \[8hours-4hours=4hours\]
Now,
\[\therefore \] C must have started \[4hours\] after A.

Hence, option ‘C’ is the correct answer.

Note: In solving these types of questions, the concept of relativity is very helpful. We have seen so many real life examples where we have seen the concept of relativity. For example:- when two trains travelling opposite to each other at some speed are verified. And after how many hours the two trains will cross each other. To find this, we use the concept of relative speed.