Multiple choice

R and S start at the same time from a place A towards a place B, at a distance of 15 km, at the speeds of 4 km/hr and 6 km/hr, respectively. S reaches B, returns immediately and meets R at C. Find the distance between A and C.

  1. 7.5 km

  2. 18 km

  3. 12 km

  4. 20 km

  5. 15 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

S travels 15km to B and then some distance back to C. R travels from A to C. Let distance AC = x. S travels 15 + (15 - x) = 30 - x. R travels x. Time is the same: (30-x)/6 = x/4. 120 - 4x = 6x => 10x = 120 => x = 12.

AI explanation

Let the time they meet be t hours after they start. Since S reaches B and turns back, the sum of the distances covered by R and S equals twice the distance from A to B. Using distance equals speed multiplied by time, we get 4t plus 6t equals 2 times 15. Solving 10t equals 30 gives t = 3 hours, so the distance from A to C is R's speed multiplied by 3, which is 4 times 3 to equal 12 km.

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