appointments.js

const appointments = [[100, 125], [200, 230], [230, 400]]

const requests = [[10, 50], [130, 210], [240, 250]]

const times = [[0]]

for (let i = 0; i < appointments.length; i++) {
	const [ra, rb] = appointments[i]
	const last = times[times.length - 1]
	last[1] = ra
	times.push([rb])
}

const results = requests.filter(([a, b]) => {
	for (let i = 0; i < times.length; i++) {
		const [x, y] = times[i]
		if (a >= x && b <= y) return true
	}

	return false
})

console.log(results)