0

$A$ and $B$ start running simultaneously on a circular track from point $O$ in the same direction. If the ratio of their speeds is $6 :1$ respectively, then how many times is $A$ ahead of $B$ by a quarter of the length of the track before they meet at $O$ for the first time?

Now I have found that $A$ and $B$ will meet at the starting point $O$ after $LCM(\frac{L}{6x},\frac{L}{x})=\frac{L}{x}$ hours where $L$ is the length of the track.
Now for the first time $A$ will be ahead of $B$ by a quarter of the length of the track will be $\frac{L}{20x}$ hour but how will I find the remaining number of times $A$ will be ahead of $B$ in total of $\frac{L}{x}$ hours. Please help !!!

Thanks in advance !!!

Ganit
  • 1,689

1 Answers1

1

Suppose $B$'s actual speed is $v$, then $A$'s relative speed wrt $B$ is $5v$. If $B$ is kept fixed at the starting point for the entire duration, then $A$ goes around the track $5$ times. Clearly he is quarter length of the track ahead of $B$ exactly $5$ times.

Edit :

The situation of $B$ moving at $v$ and $A$ moving at $6v$ (constant speeds) is equivalent to $B$ moving at $0$ (being at rest) and $A$ moving at $5v$ as only relative motion matters.

MyMolecules
  • 3,823
  • If $B$ is kept fixed at the starting point for the entire duration, then $A$ goes around the track $5$ times ==> Can you elaborate this part a little more? When both move then the relative speed is $5v$ but when you are fixing $B$ then what are you assuming the speed of $A$ to be? I am getting confused at this part. – Ganit Dec 11 '21 at 15:54
  • You might have seen such questions in Kinematics/Physics. We're viewing from reference frame of B because the motion is simple here. A's actual speed is given as $6v$, so A's relative speed is $6v-v=5v$ (and B is at rest). – MyMolecules Dec 11 '21 at 15:58
  • The situation of $B$ moving at $v$ and $A$ moving at $6v$ (constant speeds) is equivalent to $B$ moving at $0$ (being at rest) and $A$ moving at $5v$ as only relative motion matters. – MyMolecules Dec 11 '21 at 16:59