Question 7 • Common Core Precalculus - MA3112 Quarter 1
Marisol has a bicycle with wheels of 29 inches in diameter. Eliza has a bicycle with wheels of 26 inches in diameter. Both women pedal their bicycles so that the wheels turn at a constant rate of 150 revolutions per minute.Which statement compares the speeds of the two women? (Note: 1 mile = 5,280 feet)
Answer
A
Eliza travels approximately 1.34 miles per hour faster than Marisol.
B
Eliza travels approximately 2.68 miles per hour faster than Marisol.
C
Marisol travels approximately 1.34 miles per hour faster than Eliza.
D
Marisol travels approximately 2.68 miles per hour faster than Eliza.
Explanation
At the same 150 revolutions per minute, the bicycle with the larger wheels travels farther each minute. The circumference difference is π(29 − 26) = 3π inches per revolution, so Marisol travels 150 × 3π = 450π more inches per minute. Converting to miles per hour gives 450π × 60 ÷ (12 × 5,280) ≈ 1.34 miles per hour, so Marisol travels approximately 1.34 miles per hour faster than Eliza.
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