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Question

Difficulty: MediumRatios and Proportions

An aviation squadron requires 33 hours of preventive maintenance for every 88 hours of flight time. If a specific helicopter undergoes 2424 hours of preventive maintenance during a given month, what is the total number of hours logged for both flight and maintenance combined?

  1. A
    3333
  2. B
    6464
  3. 8888Answer
  4. D
    192192

Answer

The total number of hours logged is 8888.
The given ratio of maintenance to flight time is 3:83:8. Because the helicopter had 2424 hours of maintenance, we find the multiplier by dividing 2424 by 33, which is 88. We then apply this multiplier to the flight time ratio (8×8=648 \times 8 = 64 hours). To find the total combined hours, we add the maintenance hours and flight hours together: 24+64=8824 + 64 = 88.

Step-by-Step Solution

1
Find the scale factor (multiplier) by comparing the actual maintenance hours to the ratio.
24÷3=824 \div 3 = 8
This establishes how many times larger the actual numbers are compared to the base ratio.
2
Calculate the actual flight hours using the scale factor.
8×8=648 \times 8 = 64 hours of flight time
Applying the scale factor to the flight time ratio gives the actual flight time.
3
Add the actual maintenance hours and actual flight hours to find the total time.
24+64=8824 + 64 = 88 total hours
The question specifically asks for the combined total of both flight and maintenance time.

Key Concept

Solving part-to-part ratio word problems and calculating a total sum.
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Topics

Ratios and Proportions

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