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$\text{A}$ is standing $5$ m East and $4$ m North of a point $\text{P}$ while $\text{B}$ is standing $15$ m East and $24$ m North of $\text{P. A}$ walks at a speed of $1.4$ m/s while $\text{B}$ walks at a speed of $2.1$ m/s.

If $\text{A}$ and $\text{B}$ simultaneously start walking towards each other and finally meet at a point $\text{Q,}$ then find the distance $\text{PQ}.$

  1. $13$ m
  2. $12\sqrt 3$ m
  3. $15$ m
  4. $13\sqrt 2$ m
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