Answer
$608.61$ miles
Work Step by Step
Simpson's Rule states that
$T_{n}=\dfrac{1}{3}[y_0+4y_1+2y_2+..+4y_{N-3}+2y_{N-2}+4y_{N-1}+y_N]\Delta x$
Since, $\Delta t=5 \ min=\dfrac{1}{12} \ hour $
Thus, using Simpson's Rule, we have:
$S_{12}= \dfrac{1}{3}[v_0+4v_1+2v_2+..+4v_{9}+2v_{10}+4v_{11}+v_{12}]\Delta t\\=\dfrac{1}{3} (\dfrac{1}{12})[550+4(575)+2(600)+4(580)+2(610)+4(640)+2(625)+4(595)+2(590) +4(620)+2(640)+4(640)+630] \approx 608.61$
Hence, the distance traveled during the hour is approximately equal to $608.61$ miles.
