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Zorluk: OrtaInverse Proportions

A reconnaissance drone squadron currently takes 14 hours14\text{ hours} to completely map a designated tactical sector when using 66 identical drones simultaneously. If the task force commander requires the exact same sector to be mapped in 4 hours4\text{ hours}, how many total drones must be deployed?

Cevap: 21 drones

Cevap

2121 drones
The scenario describes an inverse proportion because increasing the number of active drones decreases the time required to finish the mapping. The total mapping workload is a constant 8484 drone-hours (6 drones×14 hours6\text{ drones} \times 14\text{ hours}). To complete this exact same workload in a compressed timeframe of 44 hours, a total of 2121 drones are needed (84÷484 \div 4).

Adım Adım Çözüm

1
Identify the relationship between the variables.
The number of drones and the time required are inversely proportional.
Completing a fixed amount of work faster requires proportionally more equipment.
2
Calculate the total amount of work required (the constant of variation).
6 drones×14 hours=84 drone-hours6\text{ drones} \times 14\text{ hours} = 84\text{ drone-hours}
In an inverse proportion (x×y=kx \times y = k), the product of the two variables remains constant.
3
Calculate the new number of drones required for the target time.
84 drone-hours÷4 hours=21 drones84\text{ drone-hours} \div 4\text{ hours} = 21\text{ drones}
Divide the total work constant by the new required time to solve for the missing variable.

Anahtar Kavram

Inverse proportions occur when one variable increases while another decreases such that their product remains constant (x1×y1=x2×y2x_1 \times y_1 = x_2 \times y_2).
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Konular

Inverse Proportions

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