Multiple choice

P is driving a car at a speed of 75 km per hour and it covers a distance of 1425 km. Now, P is sailing a boat and the boat takes the same time as taken by the car for travelling downstream from point A to point B and coming back to point C, which is exactly in the middle of points A and B. If the velocity of stream is 4 km/h and the speed of boat in still water is 14 km/h, then what is the distance between A and B?

  1. 180 km

  2. 185 km

  3. 215 km

  4. 220 km

  5. 245 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Car speed = 75 km/h, distance = 1425 km. Time = 1425 / 75 = 19 hours. Boat speed in still water = 14, stream = 4. Downstream speed = 18, upstream speed = 10. Let distance AB = D. Time for downstream A to B = D/18. Time for upstream B to C (D/2) = (D/2) / 10 = D/20. Total time = D/18 + D/20 = 19. (10D + 9D) / 180 = 19 => 19D / 180 = 19 => D = 180 km.

AI explanation

The car takes 1425 / 75 = 19 hours. Let the distance between A and B be 2D, so the downstream distance is 2D and the return distance is D. The downstream speed is 14 + 4 = 18 km/h and the upstream speed is 14 minus 4 = 10 km/h, making the time equation 2D/18 + D/10 = 19. Solving for D gives (10D + 9D) / 90 = 19, so 19D = 1710 and D = 90 km. The total distance between A and B is 2D, which is 180 km.

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