Question

A and B start from the same point, at the same time and run at speeds of 4m/s and 6m/s respectively
around a circular track of length 120m. After how many seconds would they meet for the first time at the
starting point?​

Answer 1

Step-by-step explanation:

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Answer 2

Given:

Speed of A = 4 m/s

Speed of B = 6 m/s

Length of circular track = 120 m

To find:

The time in seconds they meet later at the starting point for the first time.

Solution:

Here, A and B are running around a circular track.

There is no mention of whether they're running in opposite or same direction. Hence, we consider two cases:

Case-1 : When they run in opposite directions.

Case-2 : When they run in same direction.

Since, this problem involves speed, time and length, we use the formula,

$speed=\frac{distance}{time}$

or, $time=\frac{distance}{speed}$

Here, we consider relative speed, i.e., speed of a moving body with respect to another.

If both of them run in same direction, then, relative speed is the difference between the speeds at which they run.

If both of them run in opposite direction, then relative speed is the sum of speeds they run.

Case-1: When A and B run in opposite directions.

Relative speed = $6+4=10m/s$

$Time=\frac{Length}{Relative Speed}$

$Time=\frac{120}{10}=12s$

∴ After $12$ seconds, A and B will meet for the first time at the starting point if they run in the opposite directions.

Case-2: When A and B run in same direction.

Relative speed = $6-4=2m/s$

$Time=\frac{Length}{Relative Speed}$

$Time=\frac{120}{2}=60s$

∴ After $60$ seconds, A and B will meet for the first time at the starting point if they run in the same direction.

A and B will meet for the first time at the starting point after $12$ seconds when they run in the opposite directions and will meet after $60$ seconds, if they run in the same direction.