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TAE Marine. REVIEW : 20 Proof :-- .0083 xX 60 .4980 74 ao .5000, or .5 of a minute. If a boat steams 1034 (10.75) miles per hour, how far does she run in 18 mins. 30 secs.? Ans. 3.3 miles, Explanation----If she steams 10.75 miles in one hour, it will take her as many minutes to steam 1 mile as 10.75 are contained in 60 min., or 1 hour. 10.75 ) 60.000 5.58+minutes. And in 18m. 30 sec., or 18.5 min. she will run as many miles as 5.58 min., the time it takes her to make one mile, are con- tained times in 18.5, thus, 5.58 ) 18.500 3.3 OF 3.2 mules. A vessel steams 1.5 (1%) miles in 814 (8.25), or 8m. 15s. How fast is she running per hour, and how long does it take her to make a mile? Ans. 5.5 mins. to make 1 mile, and is. running 10.9 miles per hour. If she runs 1.5 miles in 8.25 mins., it will take her as many minutes to make 1 mile as 1.5 are contained times in 8.25 minutes; or, 5.5 times, or 5.5 mins..to make 1 mile; therefore, if it takes 5.5 mins. to make 1 mile, she will make as many miles in 1 hour, or 60 mins., as 5.5 are contained times in 60, or 10.9 times; hence, she is steaming 10.9, or nearly I1 miles, per hour. If a boat steams 2614 miles in 2 hrs. 8 mins, 30 secs., how fast is she running per hour, and how long does it take her to make one mile? 2614 = 26.5; 8 mins. 30 secs. = 85 mins.; 8.5 mins. is .141 of an hour, found thus: 60.) S500 ( 1412 60 250 240 100 60 --_---- Therefore, 2h. 8m. 30s. = 2.141 hrs. & hrs. - miles, 2.141 ) 26.50000 ( 1247+ miles per hour. 2141 5090 4282 8080 6423 16570 14987 12.37 ) 60.000 ( 4.8m. = 4m. 48s. 4948 10520 9896 12.37 miles per hour and 4m. 48s. per mile. 27 .T of an hour = 6 mins.; .1 of a° = 6 2 of ati hour = 12 mins.; .2 of a ° = 12". 3 of an hour = 18 mins.; .3.0f a ° = 18' -4 of an hour = 24 mins.; .4 of a ° = 24' .5 of dn hour = 30 mins.; .5 of a ° == 30' .6 of an hour = 36: mins.: 6 of a 7 == 36" 7 of an hour = 42 mins; 9 of a ~ == a 8 of an hour = 48 mins.; 8 of a ° = 48 .9 of an hour = 54 mins.; .9 of a ° = 54' Same for .t of a minute = 6 seconds; .2 of a minute = 12 seconds, etc., etc. SPEED TABLE, Running at various rates of speed the following compilation of figures show the number of minutes and fractions of a minute that it takes to make a mile. This table is given here for the express purpose of assisting the student in proving his work, and it should only be used for that purpose. Rule--Divide the number of minutes in an hour (60) by the number of miles per hour, the quotient will be either a whole or mixed number, and represents the number of mins. and fractions, also the decimals, thereof, that it takes the boat to make one mile. To get the number of seconds that the fraction, or decimal, of a minute represents, multiply it by 60 and point off. Thus, 9 into 60 mins. is 6.6 times, or 6 mins. - 36 secs.; .6 X 60 = 36.0. ' Miles per hour. Min Mins and Secs. per mile. oo V5 Oh 7. 308. Shy == 7.2y. OT, 7s 108 84 = 905 Ol. sae 7m. 38. 8y4= 685 6f° 2 6m. 5Is. > == (660 ce 6m 36s. o%4 = 0.40, Of7., 4 6m. 29s. 9% = 634i (or... 6m. I9s. 04 = 6:1 of... Ge oe 10. = G8. oe. 6m. 104 = ROS Of... 3 5m. 51s. 10% = Bt Of... 4 ..051. aoe 1034 = B50 Of... acs Sm. 358. LL = BAG OU... 5m. 27S. 14 = 63a OF 5m. 20s. 14 = Bol Of... Sim. 13s. 1y4= Rt 6f..0. 4. 5m. 6s. I2 = 5. OF sce. 5m. SIMPLE PROPORTION. This is known by navigators as the "Rule of Three." This lesson should be learned thoroughly since it is one of the most practical methods: in mathematics as applied to naviga- tion. ' A simple proportion is an expression of equality between two simple ratios. It is used to solve problems of which three terms are given, and the fourth is required. Of the three given numbers, two must always be of the same kind; and the third, of the same kind as the required term. ; A ratio is the relation between two numbers of the same unit value, expressed by the quotient of the first divided by the second. Thus, the ratio of 12 to 4 is 12 + 4 = 3. Or, the ratio of one number to another is the quotient obtained by dividing the former by the latter. Example: If 17 horses cost $4,000, what will be paid for 51 horses at the same rate? Since the rate is between 51 and 17 is 51-17, or 3, 51 horses will cost 3 times $4,000,-or $12,000. A proportion is an equation in which each number is a ratio. The equality of the two ratios may be indicated by the double colon :: The sign of ratio is the colon (:), or the sign of division with the line omitted. Thus, the ratio of 9 to 3 is expressed 9:3, or 9 + 3, or in the form of a fraction 9-3, and is read, the ratio of 9 to 3, or 9 divided by 3. The ratio of 8 to 4 is equal to that of 6 to 3, in the fol- ~