SAT Ratios, rates, proportional relationships, and units Practice Question 4 (Hard)

Question bank / Ratios, rates, proportional relationships, and units

Math · Problem-Solving and Data AnalysisHard

Gear A, which has $48$ teeth, meshes with gear B, which has $18$ teeth, so that each tooth of gear A that passes the contact point moves one tooth of gear B. If gear A turns at a constant rate of $75$ revolutions per minute, how many revolutions does gear B make in $4$ seconds?

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Answer: 40/3

In one minute, gear A moves $75 \times 48 = 3{,}600$ teeth past the contact point, so gear B also moves $3{,}600$ teeth, which is $\frac{3600}{18} = 200$ revolutions per minute. Converting to seconds, gear B makes $\frac{200}{60} = \frac{10}{3}$ revolutions per second. In $4$ seconds, it makes $4 \cdot \frac{10}{3} = \frac{40}{3}$ revolutions.

Using the ratio upside down ( $75 \cdot \frac{18}{48}$ ) gives a slower speed for the smaller gear, but a gear with fewer teeth must spin faster.

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