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Left, Right, Across....

Three men, C, D, and E, start at the same time, and from the same point in the circumference of a circlular island 71 miles around; C goes 50 miles a day, and E 40, in opposite directions round the island; and D goes along the island's diameter at the rate of of 35 miles a day. How soon will the three be again at the point of outset, reckoning the ratio of the diameter of a circle to its circumference to be 113:355?


Source: John Hunter's Text-book of Arithmetic, for the Use of Teachers, 1847