13. Xiao Li and Xiao Zhang are running at a constant speed on a circular track. They start at the same time and place, with Xiao Li running clockwise and completing a lap every 72 seconds; Xiao Zhang running counterclockwise and completing a lap every 80 seconds. A quarter-circle arc interval is marked on the track, centered at the starting point. How many seconds do they spend in the marked interval simultaneously from the start until they both return to the starting point at the same time?
【Answer】 46
【Analysis】The time required for both individuals to return to the starting point simultaneously from the start is $[72,80]=720 s$;
Assuming the circumference of the track is $720 \mathrm{~m}$, then $V_{\text {Li }}=10 \mathrm{~m} / \mathrm{s}, V_{\text {Zhang }}=9 \mathrm{~m} / \mathrm{s}$, the length of the designated interval is $720 \div 4=180 \mathrm{~m}$;
The time intervals for Xiao Li within the designated interval:
$0 \sim 9,63 \sim 81,135 \sim 153,207 \sim 225,279 \sim 297,351 \sim 369,423 \sim 441,495 \sim 513,567 \sim 585,639 \sim 657,711 \sim 720$
The time intervals for Xiao Zhang within the designated interval:
$$
0 \sim 10,70 \sim 90,150 \sim 170,230 \sim 250,310 \sim 330,390 \sim 410,470 \sim 490,550 \sim 570,630 \sim 650,710 \sim 720
$$

Overlapping time intervals: $0 \sim 9,70 \sim 81,150 \sim 153,567 \sim 570,639 \sim 650,711 \sim 720$; Total 46 seconds.