Answer
The speed of the walkway is 2 meters per second.
Work Step by Step
Let Vt be the combined speed of Liam and the walkway and let Vw be the speed of the walkway. So:
$V_t=V_w+1.5$
We know that V=D/T and the distance is 280 meters, so:
$\frac{280}{T_t}=\frac{280}{T_w}+1.5$
We also know that $T_t=T_w-60$, so we can replace Tt and find the time it takes the walkway to cover 280 meters:
$\frac{280}{T_w-60}=\frac{280}{T_w}+1.5$
$\frac{280}{T_w-60}\cdot(T_w-60)\cdot T_w=(\frac{280}{T_w}+1.5)\cdot(T_w-60)\cdot T_w$
$280T_w=(280+1.5T_w)\cdot(T_w-60)$
$280T_w=280T_w-16800+1.5T_w^2-90T_w$
$0=1.5T_w^2-90T_w-16800$
$0=1.5(T_w^2-60T_w-11200)$
$0=T_w^2-60T_w-11200$
Now, we'll use the quadratic formula, where a=1, b=-60, and c=-11200
$T_w=\frac{-(-60)\pm\sqrt{(-60)^2-4(1)(-11200)}}{2(1)}$
$T_w=\frac{60\pm\sqrt{3600+44800}}{2}$
$T_w=\frac{60\pm\sqrt{48400}}{2}$
$T_w=\frac{60\pm220}{2}$
Only the positive option will be taken into account since there can't be negative time:
$T_w=\frac{60+220}{2}$
$T_w=\frac{280}{2}=140$ seconds
Now, we can finally determine the speed of the walkway:
$V_w=280/140=2$ meters per second
