Made easy workbook

Question

If $A$ and $B$ run at $6km/hr$ and $12 km/hr$ on a circular track $6 km$ long.When will they meet for the first time if they are running in opposite direction?

Answer 1

Case 1: Same Direction

When two persons A and B are running around a circular track of length L mts with speeds of a, b m/s in the same direction
They meet each other at any point on the track is $L/(a−b)$ seconds

Case 2: Opposite Direction

When two persons A and B are running around a circular track of length L mts with speeds of a, b m/s in the same direction
They meet each other at any point on the track is $L/(a+b)$ seconds
 

Case 2 is applied here

$6 km / ( 12 km/hr + 6 km/hr)$

$(1/3)hr = 60/3 = 20 mins$

Answer 2

Time Taken to meet/catch = $\dfrac{\text{Initial distance separating them}}{\text{Relative Speed}}$

$\text{Relative Speed =} S_1 \pm S_2$ 

$\text{Relative Speed =} S_1 + S_2 \text{ ,when Both are moving towards opposite direction}$

$\text{Relative Speed =} S_1 - S_2 \text{ ,when Both are moving towards same direction}$

$∴\color{green}{\text{Time taken to meet/catch = }}$$\color{blue}{\dfrac{6\hspace{0.1cm} km}{(6+12)\hspace{0.1cm}kmph} = \dfrac{6}{18}\hspace{0.1cm}hr = \dfrac{1}{3} \hspace{0.1cm}hr = \dfrac{1}{3}\times 60 \hspace{0.1cm}min} =\color{orange}{ 20\hspace{0.1cm} min}$

Answer 3

A -> 6 Km/ h

B -> 12 Km/ h

Let they meet after " t " time.

So distance covered by A in " t " time = 6 * t

distance covered by B in " t " time = 12 * t

But total distance will be equal to 6 Km.

So,

      6 * t + 12 * t = 6

      t = $\frac{1}{3}$ hours.

     so after 20 minutes the meet.