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Question

Difficulty: MediumInverse Proportions

A naval shipyard assigns 1515 automated painting drones to coat the hull of a cruiser in exactly 2 hours2\text{ hours}. If 55 of these drones are taken offline for maintenance before the job begins, how many minutes will it take the remaining drones to complete the coating?

  1. A
    8080
  2. B
    360360
  3. 180180Answer
  4. D
    33

Answer

It will take 180 minutes for the remaining drones to complete the hull coating.
The correct answer is 180180. First, subtract the 55 offline drones from the initial 1515 to find that 1010 drones are actively working. Because the number of drones and the time required are inversely proportional, their product remains constant. The equation is 15×2=10×T215 \times 2 = 10 \times T_2, which solves to T2=3 hoursT_2 = 3\text{ hours}. Finally, converting 3 hours3\text{ hours} to minutes yields 3×60=180 minutes3 \times 60 = 180\text{ minutes}.

Step-by-Step Solution

1
Determine the number of active drones.
15−5=10 drones15 - 5 = 10\text{ drones}
The 5 offline drones cannot work, so only the remaining drones will paint the hull.
2
Set up an inverse proportion equation.
15 drones×2 hours=10 drones×T215\text{ drones} \times 2\text{ hours} = 10\text{ drones} \times T_2
Work rate problems involve inverse proportions; as the number of workers decreases, the time required increases proportionally to keep the total work constant.
3
Solve for the new time (T2T_2) in hours.
30=10×T2⇒T2=3 hours30 = 10 \times T_2 \Rightarrow T_2 = 3\text{ hours}
Dividing the total required drone-hours (3030) by the number of active drones (1010) isolates the time.
4
Convert the required time into minutes.
3×60=180 minutes3 \times 60 = 180\text{ minutes}
The question explicitly asks for the final answer in minutes, not hours.

Key Concept

Inverse Proportions
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Topics

Inverse Proportions

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