Adding a second forecasting signal

You forecast next-day returns $r$ with a signal $s$ that has correlation 0.3 with $r$. You may add a second signal $t$ and use any linear combination $as + bt$ as the forecast.

(a) Suppose $t$ has correlation 0.2 with $r$ and is uncorrelated with $s$. What is the highest correlation with $r$ you can reach?

(b) Now suppose $t$ has zero correlation with $r$ but correlation 0.5 with $s$. Does adding $t$ help? If so, give the best combination and its correlation with $r$.