Total distance required to cover by one train is 2L.
By considering one train at rest then speed of other train is (v1+v2) mile/hour = $\frac{52800}{3600}$(v1+v2)$\frac{feet}{sec}$
=$\frac{44}{3}$(v1+v2)$\frac{feet}{sec}$
As speed=$\frac{Distance}{Time}$
$\frac{44}{3}$(v1+v2)=$\frac{2L}{T}$
So,L=$\frac{22}{3}$(v1+v2)