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. 1885 Excerpt: ... increased by 6, divided by the sum of the digits, is 5. Required the number. 37. If 45 be added to a certain number of two figures, the digits will be inverted; and if the resulting number be divided by the sum of its digits, the quotient is 7 and the remainder 6. Required the number. 38. A and B can do a piece of ...
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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. 1885 Excerpt: ... increased by 6, divided by the sum of the digits, is 5. Required the number. 37. If 45 be added to a certain number of two figures, the digits will be inverted; and if the resulting number be divided by the sum of its digits, the quotient is 7 and the remainder 6. Required the number. 38. A and B can do a piece of work in m days, B and C in n days, and C and A in p days. In what time can eaoh alone perform the work? 39. A crew can row 10 miles in 50 minutes down stream, and 12 miles in an hour and a half against the stream. Find the rate in miles per hour of the current, and of the crew in still water. Let x--the rate of the crew in still water, and y = the rate of the current. Then, x + y = the rate rowing down stream, and x--y = the rate rowing up stream. Since the distance divided by the rate gives the time, we have, by the conditions, 10 5 x + y 6 12 _ 3 c-y 2 Solving these equations, x = 10, y = 2. 40. A crew can row a miles in b hours down stream, and c miles in d hours against the stream. Find the rate in miles per hour of the current, and of the crew in still water. 41. A boatman can row down stream a distance of 20 miles, and back again, in 10 hours; and he finds that he can row 2 miles against the current in the same time that he rows 3 miles with it. Required his time in going and in returning. 42. A number consists of three digits whose sum is 21. The sum of the first digit and twice the second exceeds the third by 8; and if 198 be added to the number, the digits will be inverted. Required the number. 43. A merchant has two casks of wine. He pours from the first cask into the second as much as the second contained at first; he then pours from the second into the first as much as was left in the first; and again from the first into the second as...
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