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Question

Difficulty: HardCalculating Distance

A rescue helicopter flies at a rate of 33 miles per minute for 4040 minutes to reach an extraction point. After the pickup, it flies to a hospital at a cruising speed of 120120 miles per hour for 9090 minutes. What is the total distance the helicopter traveled in miles?

  1. A
    182
  2. 300Answer
  3. C
    1,920
  4. D
    10,920

Answer

The correct answer is 300 miles, which is the sum of the 120 miles traveled in the first stage and the 180 miles traveled in the second stage.
The correct answer accurately accounts for the units in both stages of the flight. For the first stage, the units match (miles per minute and minutes), yielding 120 miles. For the second stage, 90 minutes is converted to 1.5 hours to match the miles per hour speed, yielding 180 miles. Adding them together gives 300 miles.

Step-by-Step Solution

1
Calculate the distance for the first stage by multiplying the rate by the time.
33 miles/minute × 4040 minutes = 120120 miles.
The rate is given in miles per minute and the time is given in minutes, so the units already match and no time conversion is necessary.
2
Convert the time for the second stage from minutes to hours.
9090 minutes ÷ 6060 minutes/hour = 1.51.5 hours.
The cruising speed is given in miles per hour, so the travel time must be converted to hours before calculating distance.
3
Calculate the distance for the second stage using the converted time.
120120 miles/hour × 1.51.5 hours = 180180 miles.
Multiplying the speed in mph by the time in hours yields the distance in miles.
4
Add the distances from both stages to find the total distance traveled.
120120 miles + 180180 miles = 300300 miles.
The total distance of a multi-leg journey is the sum of the distances of each individual leg.

Key Concept

Calculating multi-leg distances requiring attention to varying speed units and necessary time conversions.
Estimated Time:2m 0s
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Topics

Calculating Distance

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