Multiple choice

The time taken by car A to cover 3x km is equal to the time taken by car B to cover 2x km and the speed of car A is 15 km/hr more than that of B. If the speed of car B is increased by 4 km/hr, then find the time taken by car B to cover 170km.

  1. 2 hours

  2. 8 hours

  3. 4 hours

  4. 5 hours

  5. 11 hours
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D Correct answer
Explanation

Time A = 3x/Va, Time B = 2x/Vb. 3x/Va = 2x/Vb => Va = 1.5Vb. Also Va = Vb + 15. 1.5Vb = Vb + 15 => 0.5Vb = 15 => Vb = 30. New speed of B = 30 + 4 = 34. Time = 170 / 34 = 5 hours.

AI explanation

Since the time taken is the same, the ratio of the speeds of car A and car B is equal to the ratio of their distances, giving 3x divided by 2x, or a 3:2 ratio. We know car A is 15 km/hr faster than car B, so solving 3 parts minus 2 parts equals 15 km/hr means one part equals 15 km/hr; thus, car B's initial speed is 30 km/hr. When car B's speed increases by 4 km/hr, its new speed becomes 34 km/hr. The time taken to cover 170 km is 170 divided by 34, which equals 5 hours.

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