Examkin

Question

Difficulty: MediumInverse Proportions

A naval destroyer traveling at an average speed of 24 knots24\text{ knots} completes a specific patrol route in 3 hours3\text{ hours} and 20 minutes20\text{ minutes}. If the captain is ordered to complete the identical route in 2 hours2\text{ hours} and 30 minutes30\text{ minutes}, what average speed must the destroyer maintain?

  1. A
    18 knots18\text{ knots}
  2. 32 knots32\text{ knots}Answer
  3. C
    16 knots16\text{ knots}
  4. D
    3.2 knots3.2\text{ knots}

Answer

The destroyer must maintain an average speed of 32 knots32\text{ knots}.
The distance of the patrol route is constant, meaning the product of the initial speed and time must equal the product of the new speed and time. Converting the travel times completely to minutes gives 200 minutes200\text{ minutes} and 150 minutes150\text{ minutes}. Using the inverse proportion formula, 24×200=480024 \times 200 = 4800. Dividing this constant by the required new time of 150 minutes150\text{ minutes} gives the necessary speed of 32 knots32\text{ knots}.

Step-by-Step Solution

1
Convert both time durations entirely into minutes to ensure consistent units.
3 hours and 20 minutes=200 minutes3\text{ hours and } 20\text{ minutes} = 200\text{ minutes}, and 2 hours and 30 minutes=150 minutes2\text{ hours and } 30\text{ minutes} = 150\text{ minutes}.
Calculations involving mixed time units require a single common unit before a proportion can be accurately applied.
2
Identify the relationship between speed and time for a constant distance.
Speed and time are inversely proportional, governed by the equation S1×T1=S2×T2S_1 \times T_1 = S_2 \times T_2.
When the distance of a route remains the same, an increase in speed results in a proportional decrease in travel time.
3
Set up the inverse proportion equation and solve for the new speed (S2S_2).
24×200=S2×150  ⟹  4800=150×S2  ⟹  S2=3224 \times 200 = S_2 \times 150 \implies 4800 = 150 \times S_2 \implies S_2 = 32.
Isolating the unknown variable yields the required average speed to complete the route in the shorter timeframe.

Key Concept

Inverse Proportions in Speed and Time
Estimated Time:1m 30s
Rate this question

Topics

Inverse Proportions

More questions from this topic