Suppose R arrives at $x$ hours. J has to arrive between $x$ hrs to $x$ hrs + 15 mins. Similarly if J arrives at $y$ hours, R has to arrive between $y$ hours to $y$ hours + 15 mins. These are regions enclosed by the regions $x \leq 1, y \leq 1, y \leq x + \frac{1}{4} \;and\; y \geq x - \frac{1}{4}$. The probability is then $1 - P(\text{not meeting}) = 1 - 2(\frac{1}{2} \frac{3}{4} \frac{3}{4}) = \frac{7}{16}$.