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Zorluk: ZorCalculating Rate and Time

A rescue helicopter departs base at 09150915 hours for a distress signal 120120 miles away. It flies outbound at 160160 mph, spends 3030 minutes on scene, and returns along the same route at 120120 mph. At what time does the helicopter arrive back at the base?

  1. 1130 hoursCevap
  2. B
    1030 hours
  3. C
    1200 hours
  4. D
    1205 hours

Cevap

1130 hours
The correct arrival time is found by determining the time for each flight leg individually (Distance / Rate), ensuring decimal hours are correctly converted into minutes, adding the on-scene time, and then adding that total elapsed duration to the initial departure time.

Adım Adım Çözüm

1
Calculate the duration of the outbound flight.
0.750.75 hours (or 4545 minutes)
Using the formula Time=DistanceRate\text{Time} = \frac{\text{Distance}}{\text{Rate}}, the outbound flight takes 120160=0.75\frac{120}{160} = 0.75 hours. To convert to minutes, multiply by 6060: 0.75×60=450.75 \times 60 = 45 minutes.
2
Calculate the duration of the return flight.
11 hour (or 6060 minutes)
The helicopter returns along the same 120120-mile route at a speed of 120120 mph. 120120=1\frac{120}{120} = 1 hour.
3
Calculate the total mission duration.
135135 minutes (or 22 hours 1515 minutes)
Sum the three segments of the mission: Outbound (4545 minutes) + On-scene (3030 minutes) + Return (6060 minutes) = 135135 minutes total.
4
Determine the final arrival time based on the departure time.
11301130 hours
Add the total duration of 22 hours and 1515 minutes to the departure time of 09150915 hours. 0915+2 hours 15 minutes=11300915 + 2\text{ hours } 15\text{ minutes} = 1130 hours.

Anahtar Kavram

Calculating elapsed time using the relationship between distance and rate, converting decimal hours to minutes, and correctly summing components of a multi-leg journey.
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Konular

Calculating Rate and Time

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