Question
A gear ratio r:s is the ratio of the number of teeth of two connected gears. The ratio of the number of revolutions per minute (rpm) of two gear wheels is s:r. In the diagram below, Gear A is turned by a motor. The turning of Gear A causes Gears B and C to turn as well.
If Gear A is rotated by the motor at a rate of 100 rpm, what is the number of revolutions per minute for Gear C?
- 50
- 110
- 200
- 1000
Hint:
Hint:
- Ratio of number of revolution per minute of a two gears is inversely proportion to ration number teeth they have.
The correct answer is: 200
Explanation:
- A gear ratio r:s is the ratio of the number of teeth of two connected gears. The ratio of the number of revolutions per minute (rpm) of two gear wheels is s:r.
- We have to find what is the number of revolutions per minute for Gear C
Step 1 of 1:
Since Gear A has 20 teeth and Gear B has 60 teeth, the gear ratio for Gears A and B is 20:60.
Thus the ratio of the number of revolutions per minute (rpm) for the two gears is 60:20, or 3:1.
That is, when Gear A turns at 3 rpm, Gear B turns at 1 rpm.
Similarly, since Gear B has 60 teeth and Gear C has 10 teeth, the gear ratio for Gears B and C is 60:10, and the ratio of the rpms for the two gears is 10:60.
That is, when Gear B turns at 1 rpm, Gear C turns at 6 rpm.
Therefore, if Gear A turns at 100 rpm, then Gear B turns at 
rpm, and Gear C turns at 
rpm.
Final answer:
Hence, The number of Gear C turns at 200 rpm.
The number of teeth has an inverse relationship with revolutions per minute (rpm) when two gears are mashed. Two quantities are considered to be in inverse proportion when they are related to one another in this way, that Two quantities are considered to be in inverse proportion when they are related to one another when a rise in one quantity causes a reduction in the other and vice versa. The sum of the two provided quantities equals a constant amount in inverse proportion. The inverse proportion formula can establish a relationship between two inversely proportional quantities. Assume that x decreases when y increases and vice versa for the two numbers, x and y. Example: The relationship between time and speed is inverse. The time it takes us to travel a certain distance lowers as our speed rises. Using speed as y and time as x, where y and x are inversely proportional, the formula is written as y = k/x.s, when a rise in one quantity causes a reduction in the other and vice versa. The sum of the two provided quantities equals a constant amount in inverse proportion. The inverse proportion formula can establish a relationship between two inversely proportional quantities. Assume that x decreases when y increases and vice versa for the two numbers, x and y. Example: The relationship between time and speed is inverse. The time it takes us to travel a certain distance lowers as our speed rises. Using speed as y and time as x, y, x are inversely proportional and are technically represented as inverse proportion formula. The inverse proportional formula is written as,
y = k/x
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