\fdO'^ - Old Forge Coal Mines

92 ARITHMETIC.
(163) 2 ft. 5 in. = 29 in. ; 2 ft. 7 in. — 31 in. Stating
as a direct proportion, 29 : 31 = 2,480 : x. Now, it is easy
to see that x will be greater than 2,480. But r should be
less than 2,480, since, when a man lengthens his steps, the
number of steps required for the same distance is less;
hence, the proportion is an inverse one, and
or,
29 : 31 = ;ir : 2,480,
31:r = 71,920;
whence, x = 71,920 -r- 31 = 2,320 steps. Ans.
(154) This is evidently a direct proportion, 1 hr.
36 min. = 96 min. ; 15 hr. = 900 min. Hence,
96 : 900 = 12 : ;r,
or, 96;r= 10,800;
whence, x = 10,800 ^ 96 = 112.5 mi. Ans.
(155) This is also a direct proportion ; hence,
27.63 : 29.4 = .76 : x,
or, 27. 63 ;ir = 29. 4 X . 76 = 22. 344 ;
whence, x = 22. 344 -^ 27. 63 = . 808 + lb. Ans.
(156) 2 gal. 3 qt. 1 pt. = 23 pt. ; 5 gal. 3 qt. = 46 pt.
Hence,
23 : 46 = 5 : 4r,
or, 23.*-= 46 X 5 = 230;
whence, ;r = 230 -^ 23 = 10 days. Ans.
(157) Stating as a direct proportion, and squaring the
distances, as directed by the statement of the example,
since this
6' : 12" = 24 : ;r. Inverting the second couplet,
is an inverse proportion,
6' : 12' = X : 24.
Dividing both terms of the first couplet (see Art. 310)
by 6
1» : 2* = 4.' : 24; or 1 : 4 = ^r : 24;
whence, 4 .r = 24, or x = 6 degrees.
Ans.