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The Long Chase is On

Three men, C, D, and E, start at the same time, and from the same point in the circumference of a circle 71 miles round; 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 35 miles a day. How soon will the three be again at the point of outset, reckoning the ratio of the diameter of the circle to its circumference to be 113:355?


Source: J. Hunterís Text-book of Arithmetic, for the Use of Teachers, 1847