This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1890 Excerpt: ...Fig. 1. in length. Then the arc MA will be 12a; minute-spaces in length. But MA = MH + HA = 20 + x... 12x = 20 + x, whence x--lft, and 20 + x = 21. Ans. The hands are together at 21T minutes past iv. Fio. 2. II. Let CA be the position of the minute-hand, and OB be the position of the hour-hand when the hands are at ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1890 Excerpt: ...Fig. 1. in length. Then the arc MA will be 12a; minute-spaces in length. But MA = MH + HA = 20 + x... 12x = 20 + x, whence x--lft, and 20 + x = 21. Ans. The hands are together at 21T minutes past iv. Fio. 2. II. Let CA be the position of the minute-hand, and OB be the position of the hour-hand when the hands are at right angles. Let x represent the number of minutespaces in the arc HB. Then 12a; represents the number of minute-spaces in the arc MA. But MA also equals 5-f x... (Ax. 1.) 12z=5--x, whence x=ft, and 12. -=5-1. Ans. The hands form a right angle at 5ft minutes past iv. But the hands will be again at right angles between iv and v, when the minute-hand is 15 minute-spaces ahead of the hour-hand. If, as before, the number of minute-spaces in the arc HB--x, then the number of minutespaces in the arc M HB A is 2 = --x... x--3ft and 12a; = 38. A ns. The hands are at right angles a second time between iv and v at 38 minutes past iv. III. Let CB be the position of the hour-hand, and CA be the position of the minute-hand when the hands are opposite. If HB = X, then MHBA = 12x. But M HB A also equals 50 + x... I2x--50 + X..-. x= 4jST, and 12z = 54-ft, 4ws. The hands are opposite at 54T6T minutes past IV. Fig. 4. IV. Let CB and CA be the positions of the hands when vu is midway between them; also, let HB-x... DB = 15--x, because HD = 15, and DB = DH- . Since DA = DB, .. DA = 15-x, whence MDA =35 + DA = 50- . But MDA = 12x..'.12x = 50-x, whence x = 3f, and 12a: = 46T2T. Fiq. 5. Ans. The hands are equidistant from vu at 46 minutes past IV. PROBLEMS INVOLVING TWO OR MORE UNKNOWN QUANTITIES. 305.--9. A and work together for 2 hours, after which leaves, and A completes the task in 6 h...
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