Question
Two cars, A and B, are traveling in the same direction
on a highway. The ratio of their speeds is 3:4. If both cars increase their speeds by 15 km/h, the ratio of their speeds becomes 7:9. What is the original speed of the faster car (Car B)?Solution
Let the original speeds of Car A and Car B be 3x and 4x, respectively. After increasing speeds: Car A's new speed = 3x + 15 Car B's new speed = 4x + 15 New ratio = (3x + 15) : (4x + 15) = 7 : 9 Cross-multiplying: 9(3x + 15) = 7(4x + 15) 27x + 135 = 28x + 105 135 - 105 = 28x - 27x 30 = x Therefore, the original speed of Car B (the faster car) is 4x = 4 * 30 = 120 km/h Ans. a
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