Multiple choice

Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in opposite directions, they meet in 9/7 hours. If they go in the same direction, they meet after 9 hrs. Find their speeds (in km/hr).

  1. 40, 30

  2. 40, 50

  3. 60, 30

  4. 50, 60
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A Correct answer
Explanation

Let speeds be x and y. Opposite: (x+y) = 90 / (9/7) = 70. Same direction: (x-y) = 90 / 9 = 10. Adding: 2x = 80 -> x = 40. Subtracting: 2y = 60 -> y = 30.

AI explanation

Let the speeds of the two cars be x km/hr and y km/hr. Using the relative speed concept, when moving in opposite directions, their relative speed is (x + y), which gives the equation (x + y) = 90 divided by 9/7, so x + y = 70. When moving in the same direction, their relative speed is (x - y), giving the equation (x - y) = 90 divided by 9, so x - y = 10. Solving these equations by adding them yields 2x = 80, meaning x = 40; substituting x into the first equation gives y = 30. Therefore, their speeds are 40 km/hr and 30 km/hr.

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