1. A lathe having a 5-step pulley is driven by a belt, assumed to be crossed, from a pulley of the same size on the countershaft. The countershaft is to have a constant speed, and the lathe is to have speeds of 60 rpm and 135 rpm when the belt is on the steps either side of the center step. If the minimum speed is 40 rpm and the smallest diameter is 4 in., find the proper speed of the countershaft, maximum speed of the lathe, and the diameter of all steps on the pulleys.
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