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Difficulty: MediumRelative Motion and Catch-Up Scenarios

Two rescue helicopters, operating in the same coastal region, are 360360 miles apart. They take off at the same time and fly directly toward each other. Helicopter A flies at a constant speed of 110110 mph, and Helicopter B flies at a constant speed of 130130 mph. How many minutes will it take for the two helicopters to meet?

  1. A
    1080
  2. B
    180
  3. 90Answer
  4. D
    110

Answer

It will take 90 minutes for the two helicopters to meet.
The correct answer is 90. When two objects travel directly toward each other, their relative rate is the sum of their individual speeds. The combined speed is 110+130=240110 + 130 = 240 mph. The time to meet is the total distance divided by the relative speed: 360/240=1.5360 / 240 = 1.5 hours. Finally, to convert hours to minutes, multiply by 60: 1.5×60=901.5 \times 60 = 90 minutes.

Step-by-Step Solution

1
Calculate the combined relative speed of the two helicopters.
110+130=240110 + 130 = 240 mph
When two objects are moving directly toward each other, their relative speed is the sum of their individual speeds.
2
Calculate the time in hours it takes for them to meet.
360/240=1.5360 / 240 = 1.5 hours
Time is equal to the total distance divided by the relative speed.
3
Convert the time from hours to minutes.
1.5×60=901.5 \times 60 = 90 minutes
The question specifically asks for the time in minutes.

Key Concept

Relative Motion and Time Conversion
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Topics

Relative Motion and Catch-Up Scenarios

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