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Difficulty: EasyCalculating Distance

A coast guard rescue helicopter flies directly toward a distressed vessel at a constant speed of 120 miles per hour120\text{ miles per hour}. If the flight takes exactly 45 minutes45\text{ minutes}, what is the total distance traveled by the helicopter?

  1. 90 miles90\text{ miles}Answer
  2. B
    5,400 miles5,400\text{ miles}
  3. C
    54 miles54\text{ miles}
  4. D
    900 miles900\text{ miles}

Answer

The total distance traveled by the helicopter is 90 miles90\text{ miles}.
The correct answer accurately converts the 45 minutes45\text{ minutes} of flight time into 0.75 hours0.75\text{ hours}, and then applies the distance formula (D=R×TD = R \times T) to find 120×0.75=90 miles120 \times 0.75 = 90\text{ miles}.

Step-by-Step Solution

1
Convert the flight time from minutes to hours.
45 minutes=4560 hours=0.75 hours45\text{ minutes} = \frac{45}{60}\text{ hours} = 0.75\text{ hours}.
The speed is given in miles per hour, so the time must also be in hours to calculate the distance correctly.
2
Calculate the distance using the formula Distance=Rate×Time\text{Distance} = \text{Rate} \times \text{Time}.
120 miles per hour×0.75 hours=90 miles120\text{ miles per hour} \times 0.75\text{ hours} = 90\text{ miles}.
Multiplying the constant speed by the total time in hours gives the total distance traveled.

Key Concept

To find distance, multiply the rate of speed by the time traveled, ensuring that the units of time match the units in the speed rate.
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Topics

Calculating Distance

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