A circular gear with a diameter of 25 cm is mounted directly over another circular gear with a diameter of 100 cm. Both gears run on the same axle at their exact centers and each gear has a single notch at the 12 o'clock position. At the same moment, the gears start to rotate at the same rate in cm/s, with the larger gear moving clockwise and the smaller gear moving anticlockwise.
How far in centimeters will the notch on the larger gear have moved the second time the notches pass each other?
Correct answer: E
Explanation
The large gear has a circumference that is 4 times the small gear.
If the rate in cm/s is equal, the small gear rotates 4 times as many degrees per second.
The first meeting happens when the small gear rotates 4/5 of a circle and the large gear rotates 1/5 of a circle. At the second meeting, the large gear will have rotated a total of 2/5 of a circle.
2/5*2*pi*R = 40*pi centimeters.
The answer is E.
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AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.