Geometry

Triangle PUQ is similar to  triangle TUS

ST = 3 / (2 + 3) * SR  =  (  3/5) * (20) =  12

So ST / PQ = 12 / 20  =  3/ 5

Then  the altitude of PUQ =  QV

And the altitude of TUS = RV

So  RV  /  QV =  3 / 5

And QV / QR =  QV / ( QV + RV)  =   5 / ( 5 + 3) =  5 / 8

So QV = (5/8)QR

And triangle  QUV is similar to  triangle QSR

So

UV / QV =  SR / QR 

UV /  (5/8)QR = 20 / QR

UV  / (5/8) = 20

UV  = (5/8) (20)    =  12.5