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Difficulty: HardRatios and Proportions

In a mechanical winch system, three interlocking gears are used to lift cargo. Gear A completes 44 revolutions for every 33 revolutions Gear B completes. Gear B completes 22 revolutions for every 55 revolutions Gear C completes. If Gear C spins at a rate of 120120 revolutions per minute, how many revolutions will Gear A complete in one minute?

  1. A
    4848
  2. 6464Answer
  3. C
    9090
  4. D
    160160

Answer

Gear A will complete 6464 revolutions in one minute.
The correct answer successfully steps through the proportion chain. First, finding Gear B's revolutions (120×25=48120 \times \frac{2}{5} = 48), and then using Gear B's value to find Gear A's revolutions (48×43=6448 \times \frac{4}{3} = 64).

Step-by-Step Solution

1
Find the number of revolutions for Gear B using its ratio with Gear C.
Gear B completes 4848 revolutions.
The ratio of Gear B to Gear C is 2:52:5. Setting up the proportion B120=25\frac{B}{120} = \frac{2}{5} gives B=120×25=48B = \frac{120 \times 2}{5} = 48.
2
Find the number of revolutions for Gear A using its ratio with Gear B.
Gear A completes 6464 revolutions.
The ratio of Gear A to Gear B is 4:34:3. Setting up the proportion A48=43\frac{A}{48} = \frac{4}{3} gives A=48×43=64A = \frac{48 \times 4}{3} = 64.

Key Concept

Multi-step ratios and proportions
Estimated Time:1m 0s
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Topics

Ratios and Proportions

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