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Zorluk: OrtaCalculating Distance

A Coast Guard search and rescue helicopter departs its base and flies toward a distress signal at a steady speed of 140 knots140\text{ knots} for 45 minutes45\text{ minutes}. Upon arriving at the scene, the helicopter hovers in place for 15 minutes15\text{ minutes} to hoist a survivor. It then flies directly to a coastal hospital at a steady speed of 160 knots160\text{ knots}, arriving after 1 hour and 15 minutes1\text{ hour and } 15\text{ minutes}. What is the total distance traveled by the helicopter during this mission?

  1. 305 nautical miles305\text{ nautical miles}Cevap
  2. B
    300 nautical miles300\text{ nautical miles}
  3. C
    247 nautical miles247\text{ nautical miles}
  4. D
    200 nautical miles200\text{ nautical miles}

Cevap

305 nautical miles305\text{ nautical miles}
The correct answer is found by determining the distance of each flight leg separately and adding them together. First, convert the times into hours: 45 minutes45\text{ minutes} is 0.75 hours0.75\text{ hours}, and 1 hour 15 minutes1\text{ hour } 15\text{ minutes} is 1.25 hours1.25\text{ hours}. Then, apply the formula Distance=Rate×Time\text{Distance} = \text{Rate} \times \text{Time}. The first leg is 140 knots×0.75 hours=105 nautical miles140\text{ knots} \times 0.75\text{ hours} = 105\text{ nautical miles}. The hover adds 00 distance. The final leg is 160 knots×1.25 hours=200 nautical miles160\text{ knots} \times 1.25\text{ hours} = 200\text{ nautical miles}. Adding these segments together (105+200105 + 200) yields a total distance of 305 nautical miles305\text{ nautical miles}.

Adım Adım Çözüm

1
Convert the travel time of the first leg from minutes to hours.
45 minutes=45/60=0.75 hours45\text{ minutes} = 45 / 60 = 0.75\text{ hours}
Speed is given in knots (nautical miles per hour), so the time must be represented in hours.
2
Calculate the distance traveled during the first leg.
140 knots×0.75 hours=105 nautical miles140\text{ knots} \times 0.75\text{ hours} = 105\text{ nautical miles}
Distance is equal to rate multiplied by time.
3
Determine the distance traveled during the hover phase.
0 nautical miles0\text{ nautical miles}
The helicopter is stationary while hovering, so no distance is covered.
4
Convert the travel time of the final leg to hours.
1 hour and 15 minutes=1+(15/60)=1.25 hours1\text{ hour and } 15\text{ minutes} = 1 + (15 / 60) = 1.25\text{ hours}
Consistent units are required to accurately apply the distance formula.
5
Calculate the distance traveled during the final leg.
160 knots×1.25 hours=200 nautical miles160\text{ knots} \times 1.25\text{ hours} = 200\text{ nautical miles}
Using the distance formula again for the final phase of the journey.
6
Sum the distances from all phases of the mission.
105+0+200=305 nautical miles105 + 0 + 200 = 305\text{ nautical miles}
The total mission distance is the sum of the distances covered in each individual segment.

Anahtar Kavram

Calculating distance across multiple segments by converting time to consistent units and applying the Distance = Rate × Time formula for each segment.
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Calculating Distance

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