Answer:
37,800 meters (or 37.8 km)
Step-by-step explanation:
To solve the problem, begin by defining the variables:
[tex]v_D = 100 \text{ m/min (Devi's speed)}\\\\v_K = 80\text{ m/min (Kumar's speed)}\\\\v_L = 75\text{ m/min (Li Ting's speed)}[/tex]
We are given that Devi meets Li Ting 6 minutes after passing Kumar:
To find the distance Devi travels before passing Kumar, we multiply Devi's speed by the time it takes:
[tex]d_D = v_D \times t = 100t \text{ meters}[/tex]
Similarly, to find the distance Kumar travels being passing Devi, we multiply Kumar's speed by the time it takes:
[tex]d_K = v_K \times t = 80t \text{ meters}[/tex]
Since they are travelling in opposite directions towards each other, and pass each other at the same point:
[tex]\text{Distance between Town A and Town B}=100t + 80t \\\\\text{Distance between Town A and Town B}= 180t \text{ meters}[/tex]
To find the distance Devi travels to meet Li Ting, we multiply Devi's speed by the time it takes:
[tex]d_{D,LT} = v_D \times (t + 6) = 100(t + 6) \text{ meters}[/tex]
To find the distance Li Ting travels to meet Devi, we multiply Li Ting's speed by the time it takes:
[tex]d_{L} = v_L \times (t + 6) = 75(t + 6) \text{ meters}[/tex]
Since they are travelling in opposite directions towards each other, and meet at the same point:
[tex]\text{Distance between Town A and Town B}=100(t+6) + 75(t+6)\\\\\text{Distance between Town A and Town B}= 175t +1050\text{ meters}[/tex]
Now we have two equations for the distance between Town A and Town B. Set the two equations equal to each other and solve for t:
[tex]180t=175t+1050\\\\5t=1050\\\\t=210\text{ minutes}[/tex]
Now, substitute t = 210 into one of the equations and solve for distance (D). Let's use D = 180t:
[tex]D=180(210)\\\\D=37800\text{ meters}[/tex]
Therefore, the distance between Town A and Town B is:
[tex]\Large\boxed{\boxed{37800 \text{ meters}}}[/tex]
In kilometers, the distance is 37.8 km.