Multiple choice

A cargo ship X takes (d - 6) hours to travel a certain distance downstream and (d + 6) hours to travel the same distance upstream. The speed of ship X in still water is 20 km/hr. Another cargo ship Y has a speed in still water equal to the speed of the river current, which is 8 km/hr. Find the distance (in km) covered by ship Y downstream in (d + 4) hours, assuming both ships are operating in the same river conditions.

  1. 245 km

  2. 258 km

  3. 285 km

  4. 304 km

  5. 348 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance be D. Downstream speed = 20+8=28. Upstream = 20-8=12. D/28 = d-6, D/12 = d+6. D = 28(d-6) = 12(d+6). 28d - 168 = 12d + 72. 16d = 240. d = 15. D = 28 * (15-6) = 28 * 9 = 252. Ship Y speed = 8. Downstream = 8+8=16. Distance in (d+4) = 15+4=19 hours. Distance = 16 * 19 = 304.

AI explanation

Using the distance formula, the downstream distance equals the upstream distance, so 20 plus 8 multiplied by the quantity d minus 6 equals 20 minus 8 multiplied by the quantity d plus 6. Simplifying this gives 28d minus 168 equals 12d plus 72, which leads to 16d equals 240 and d equals 15. Ship Y's downstream speed is its still water speed of 8 plus the current of 8, totaling 16 kmph, so multiplying by the time of d plus 4, which is 19 hours, gives a distance of 304 km.

Keep practicing — related questions