Multiple choice

Two cars, Car A and Car B, start from opposite points at the same time. The speeds of both cars form a geometric progression (GP). Car A starts with a speed of 80 km/h, while Car B starts with a speed of 88 km/h. Each subsequent hour, the speed of both the cars decreases by a factor of 0.5. If the distance between the starting points of Car A and Car B is 315 kilometres, find the time it takes for them to meet.

  1. 4 hours

  2. 6 hours

  3. 8 hours

  4. They never meet.

  5. a
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A Correct answer
Explanation

Speeds form a GP with r = 0.5. Speed of A at hour n: 80 * (0.5)^(n-1). Speed of B at hour n: 88 * (0.5)^(n-1). Sum of distances covered in 4 hours: Sum = (a(1-r^n))/(1-r). For A: 80(1-0.5^4)/(1-0.5) = 160(0.9375) = 150. For B: 88(1-0.5^4)/(1-0.5) = 176(0.9375) = 165. Total distance = 150 + 165 = 315.

AI explanation

The speeds of both cars form a geometric progression with a common ratio of 0.5. Using the sum of a geometric series, the total distance covered by both cars after n hours is (80 + 88) multiplied by (1 - 0.5^n) divided by (1 - 0.5). Setting this equal to 315 gives 168 multiplied by (1 - 0.5^n) equals 315, so 0.5^n equals 0.0625. Since 0.5 raised to the 4th power equals 0.0625, they meet after 4 hours. The result is 4 hours.

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