Elementary arithmetic, with brief notices of its history... by Robert Potts.

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7. Translate and solve the problem:XaXKEcs EL.LL?AWV, Kpovo VOLe /11O 6i UaTa aoL&,
Kall 0aT4ua, ical tb Oe'ap &e1TrepoZo 7ro'aos.
nXI7j0eL 8e Kpf77Tpa Wv' H/&ao-t aetlov 0o6/xa,
Kal Aalbv Trpio'ois, Kai 7ria'pEart O'vap:
'ApKlov e' &pa LS -TrAoai Tr Tua, et 8'&,ua rav7ra,
Kal o-Ta/ua, Kal 7yAP.Lat iKa Oerap, eare ~ro'ls.
XXXIII.
1. If one person take steps of 29 inches each and another person
steps of 31 inches; if the latter take 59, and the former 61 in a minute;
what is the difference of time between each person walking a mile?
2. A and B walk to meet each other from two places 100 miles
distant. A walks 6 miles an hour and B 4 miles an hour. At what
point on the road do they meet, and at what two times are they 50
miles apart from each other?
3. How long will a column of 10,000 men, 4 deep, require to march
through a defile of 5 miles at the rate of 75 paces of 2 feet each in one
minute, supposing each rank of 4 men to occupy 20 inches in depth?
4. If two trains be moving in contrary directions at the rate of 30
miles an hour, and each of them be 88 yards long, how long will they
take to pass each other? But if one of the trains 88 yards long was
moving 30 miles an hour, and the other 120 yards long was moving
40 miles an hour, find the time in which they would pass one another.
5. Two trains 100 yards and 150 yards long respectively, are
moving in the same direction at the rates of 30 and 40 miles an hour.
In what time will one pass the other?
6. If sound travel through air at the rate of 1,130 feet per second,
through water at 4,700 feet per second, and through land at 7,000 feet
per second, in what times could sound be transmitted a distance of 6
miles through each of these media?
7. A person saw the flash of a gun fired from a ship at sea distant
a mile and 480 yards, and 5 seconds afterwards saw the flash of another
gun fired from another ship in a line between the first ship and himself, and two seconds still later heard two reports simultaneously. Find.
the distance between the ships.
8. A person shooting at a target at a distance of 500 yards hears
the bullet strike the target 4 seconds after he fired. A spectator equally
distant from the target and the shooting station hears the shot strike
2- seconds after he heard the report. Find the velocity of sound.
9. If the velocity of electricity be 288,000 miles per second, what
time would it take to travel round the earth, whose circumference is.
about 24,900 miles?
10. While Roemer was engaged in observing the eclipses of Jupiter's satellites, he found that when Jupiter was in opposition the
eclipses happened 8' 13" earlier than they should according to the
astronomical tables, and when Jupiter was in conjunction these eclipses