The figure shows the arch of the parabola $y = 3x - x^2$ above the $x$-axis, between $x = 0$ and $x = 3$, and a straight line $y = mx$ through the origin, with $0 < m < 3$. The line meets the parabola again at a point $P$, and it cuts the region under the arch into two parts: an upper part, between the arch and the line, and a lower part, between the line, the arch beyond $P$ and the $x$-axis. Find the area of the upper part in terms of $m$ first. For which value of $m$ do the two parts have equal areas?

Fig. 1: The arch of the parabola y = 3x - x^2 above the x-axis from x = 0 to x = 3. A straight line through the origin with a small positive slope meets the arch again at a point P. The part of the arch above the line is shaded in one colour and the part below the line in another. The line is drawn in one sample position only.