2020 Cayley Problem 22

In the diagram, points S and T are on sides QR and PQ, respectively, of \triangle PQR so that PS is perpendicular to QR and RT is perpendicular to PQ. If PT = 1, TQ = 4, and QS = 3, what is the length of SR?

\textbf{(A)}\ 3\quad \textbf{(B)}\ \frac{11}{3}\quad \textbf{(C)}\ \frac{15}{4}\quad \textbf{(D)}\ \frac{7}{2}\quad \textbf{(E)}\ 4

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Full credit to this problem is given to the CEMC, you may view all Cayley contests here.