Part 53

(253) 79·26 feet.

(254) 9 plus 9 plus 9 plus 3 = 30, 39-9/9 = 40, or 28-2/1 = 30, 28 plus 12 = 40.

(255) 5d.

(256) 196078431372549. Method: Keep on adding imaginary 3’s until it comes out thus--17)33/17(196078431372549

To prove it:-- 196078431372549 17 ---------------- Proof-- 3333333333333333

(257)

28 eggs. Method: 1½ hens lay 1½ eggs in 1½ days 1½ " " 3 " " 3 " 3 " " 6 " " 3 " 3 " " 2 " " 1 " 6 " " 4 " " 1 " 6 " " 28 " " 7 "

(258) Tom, 4s. 6d. per day; Bill, 3s.

(259) 1000.

(260) 1 inch remainder.

(261) [Illustration]

(262) 393,213 shillings.

(263) 2/9.

(264) 9½.

(265) 4 seconds.

(266) Loses £50.

(267) He will never enter the water, because the frog’s jump, at any time, is only half-way to the water.

(268) [Illustration]

(269) 1⅔ minutes.

(270) 49 years.

(271) 3 minutes.

(272)

| | | | | -----------+----------+-----+-----+-- A B C D E

Let A be starting point of Orderly; B be starting point of General; C be point at which Orderly returns to his place, the rear having marched 50 miles to this point; D be point at which Orderly delivers his despatches; E be destination of front rank or General of Army.

Let x eq. number of miles between C and D.

Then AD eq. (50 plus x) miles; BD eq. (25 plus x) miles; DE eq. (25 minus x) miles; and AD plus DC eq. (50 plus 2x) miles, and is the total distance the Orderly travels.

Now Orderly rides from A to D, while General marches from B to D, and Orderly returns from D to C, while General marches from D to E, and Orderly and Army travel at a uniform rate.

∴ AD : BD :: DC : DE or 50 plus x : 25 plus x :: x : 25-x ∴ 1250-25x-x^2 eq. 25x plus x^2 Whence x eq. 15.45 plus. ∴ Orderly rides 50 plus 30.9 plus eq. 80.9 plus eq. 80 miles 1587 yards nearly.