Examkin

Question

Difficulty: HardInverse Proportions

A military logistics officer must calculate operational timelines based on available resources. Connect each situation below to its correctly calculated duration. Assume all rates are constant and inversely proportional.

  • A runway repair takes 14 hours when 18 engineers are assigned. Time required if 21 engineers are tasked with the exact same repair.12 hours
  • A patrol boat traveling at 36 knots completes a coastal route in 4.5 hours. Time required to complete the route at a reduced speed of 27 knots.6 hours
  • Fifteen identical extractor fans ventilate a bunker complex in 6 hours. Time required if only 10 of these fans are operational.9 hours
  • A forward base's fuel cache can power 16 standard generators for 45 hours. Time the cache will last if 24 generators are running simultaneously.30 hours

Answer

The scenarios pair correctly with 12 hours, 6 hours, 9 hours, and 30 hours respectively based on their constant products.
Each scenario involves an inverse relationship where the product of the two given quantities forms a constant. Dividing this constant by the new condition yields the correctly paired time.

Step-by-Step Solution

1
Identify the relationship for each scenario.
All four scenarios represent inverse proportions, meaning the product of the two variables (e.g., workers and time, speed and time) remains constant (x1×y1=x2×y2x_1 \times y_1 = x_2 \times y_2).
When one variable increases (like adding more workers or driving faster), the time required decreases proportionally.
2
Calculate the constant product for each individual scenario.
Engineer-hours: 18×14=25218 \times 14 = 252. Distance: 36×4.5=16236 \times 4.5 = 162. Fan-hours: 15×6=9015 \times 6 = 90. Generator-hours: 16×45=72016 \times 45 = 720.
This establishes the total amount of work, distance, or resource available before the change in variables.
3
Divide each constant product by the new given variable to find the new time.
Runway: 252÷21=12252 \div 21 = 12. Boat: 162÷27=6162 \div 27 = 6. Fans: 90÷10=990 \div 10 = 9. Generators: 720÷24=30720 \div 24 = 30.
Applying the inverse proportion formula (y2=kx2y_2 = \frac{k}{x_2}) isolates the unknown time.

Key Concept

Inverse Proportions in Work, Speed, and Resource Rates
Rate this question

Topics

Inverse Proportions

More questions from this topic