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Zorluk: OrtaBasic Ratios

A mechanical winch uses a gear system where the driving gear and the driven gear have a revolution ratio of 4:74:7. If the driving gear completes 124124 revolutions during a lifting operation, how many revolutions does the driven gear complete?

Cevap: 217 revolutions

Cevap

217
The correct answer is found by setting up a direct proportion based on the 4:7 ratio. Since the driving gear's 4 parts scale up to 124 actual revolutions, the scale factor is 31 (124 ÷ 4). Multiplying the driven gear's 7 parts by this same scale factor yields 217 revolutions.

Adım Adım Çözüm

1
Identify the known ratio
Driving : Driven = 4 : 7
This establishes the proportional relationship between the two gears.
2
Set up a proportion using the known quantity
4 / 7 = 124 / x
We know the driving gear completes 124 revolutions, which corresponds to the '4' in the ratio.
3
Find the scale factor
124 ÷ 4 = 31
This tells us how many times greater the actual operation is compared to the base ratio.
4
Calculate the unknown quantity
7 × 31 = 217
Applying the same scale factor to the driven gear maintains the proportional relationship.

Anahtar Kavram

Solving for an unknown part in a part-to-part relationship using scale factors.
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Basic Ratios

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