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Zorluk: OrtaDirect Proportions

Determine the correct numerical values to complete the statement.

Cevap:An aviation mechanic calibrates 88 flight instruments in 33 hours. If a squadron requires 2020 instruments to be calibrated, and the mechanic works at the same constant rate, it will take 【7】 hours and 【30】 minutes to complete the task.

Cevap

It will take 7 hours and 30 minutes.
Because the work rate is constant, the number of instruments calibrated is directly proportional to the time taken. Setting up the proportion 8/3 = 20/x yields x = 7.5 hours. Converting the remaining 0.5 hours to minutes gives 30 minutes, resulting in a total required time of 7 hours and 30 minutes.

Adım Adım Çözüm

1
Set up a direct proportion comparing the number of instruments to the time in hours.
8 instruments3 hours=20 instrumentsx hours\frac{8 \text{ instruments}}{3 \text{ hours}} = \frac{20 \text{ instruments}}{x \text{ hours}}
When a rate is constant, the ratio of work completed to time taken remains equivalent.
2
Cross-multiply the terms to create a linear equation.
8x=3×208x = 3 \times 20
Cross-multiplying is the standard algebraic method to solve for an unknown in a proportional relationship.
3
Simplify the equation and solve for xx.
8x=60⇒x=608=7.5 hours8x = 60 \Rightarrow x = \frac{60}{8} = 7.5 \text{ hours}
Isolating xx provides the total required time expressed in hours.
4
Convert the decimal portion of the hours into minutes.
0.5 hours×60 minutes/hour=30 minutes0.5 \text{ hours} \times 60 \text{ minutes/hour} = 30 \text{ minutes}
The question specifically requires the final answer to be formatted in hours and minutes.

Anahtar Kavram

Direct proportions with unit conversion
Tahmini Süre:1m 30s
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Konular

Direct Proportions

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