Multiple choice

Car A starts from M and car B starts from N at the same time. M and N are 64 km apart. When they move in the same direction, they meet in 8 hours and when they move in opposite directions, they meet in 4 hours. What are the speeds of the cars?

  1. A - 10 km/hr, B - 6 km/hr

  2. A - 12 km/hr, B - 4 km/hr

  3. A - 14 km/hr, B - 14 km/hr

  4. A - 16 km/hr, B - 10 km/hr

  5. A - 20 km/hr, B - 16 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speeds be u and v. Relative speed in same direction is u - v = 64/8 = 8. Relative speed in opposite direction is u + v = 64/4 = 16. Solving u - v = 8 and u + v = 16 gives 2u = 24, so u = 12, and v = 4.

AI explanation

Let the speeds of the two cars be x km/hr and y km/hr, with x being the faster car. When moving in the same direction, their relative speed is x minus y, and the equation becomes 64 divided by x minus y equals 8, meaning x minus y equals 8. When moving in opposite directions, their relative speed is x plus y, and the equation becomes 64 divided by x plus y equals 4, meaning x plus y equals 16. Solving the two equations simultaneously gives 2x equals 24, so x equals 12, and consequently y equals 4, meaning the speeds are 12 km/hr and 4 km/hr.

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