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Difficulty: EasyRelative Motion and Catch-Up Scenarios

Two cars leave a parking lot at the same time and travel in opposite directions on a straight highway. One car travels at a constant speed of 4040 mph, and the other car travels at a constant speed of 5050 mph. How many hours will it take for the two cars to be exactly 270270 miles apart?

  1. 3Answer
  2. B
    6
  3. C
    27
  4. D
    30

Answer

It will take 3 hours for the cars to be 270 miles apart.
The correct answer is 3. Since the cars are traveling in opposite directions, their speeds are added to find the total rate at which they are separating: 40 mph+50 mph=90 mph40 \text{ mph} + 50 \text{ mph} = 90 \text{ mph}. To find the time it takes to separate by 270270 miles, divide the total distance by the combined relative speed: 270÷90=3270 \div 90 = 3 hours.

Step-by-Step Solution

1
Determine the relative speed of the two cars.
40+50=9040 + 50 = 90 mph
When two objects move in opposite directions away from each other, their relative speed is the sum of their individual speeds.
2
Calculate the time required to reach the target distance.
270÷90=3270 \div 90 = 3 hours
Time equals total distance divided by the relative speed (T=D÷RT = D \div R).

Key Concept

Relative Motion (Opposite Directions)
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Topics

Relative Motion and Catch-Up Scenarios

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