An escalator has 60 visible steps.

The first kid's movement is aided by the escalator, while the second kid's movement is opposed by it. Since they reach the top at the same time, the sum of the steps climbed by both kids must equal twice the total length of the escalator (60 * 2 = 120), but since the second kid is fighting a downward flow, the relative distance covered is the sum of the escalator's displacement and the kid's effort.

Step-by-step Derivation:
Step 1: Define variables. Let L = 60 (total visible steps). Let v_k be the speed of the kids (steps per unit time) and v_e be the speed of the escalator (steps per unit time).
Step 2: Analyze the first kid. The first kid climbs 15 steps. The escalator moves the remaining 45 steps (60 - 15). The time taken is t = 15 / v_k. In this time, the escalator moved 45 steps, so v_e = 45 / t = 45 / (15 / v_k) = 3 * v_k.
Step 3: Analyze the second kid. The second kid moves against the escalator. The net speed is (v_k - v_e) if the escalator is moving down. However, the problem states the second kid reaches the top at the same instant. For the second kid to move upward while the escalator moves downward, their speed v_k must be greater than v_e. Wait, let's re-evaluate the relative speed: 'at the same relative speed' means the speed relative to the steps is the same.
Step 4: Let x be the steps the second kid climbs. The distance the second kid covers relative to the ground is L = 60. The distance covered relative to the escalator is x. Because the escalator is moving down, the distance the escalator moves the kid down is v_e * t. Thus, 60 = x - (v_e * t).
Step 5: Substitute the values from the first kid. We know t = 15 / v_k and v_e = 3 * v_k.
Step 6: 60 = x - (3 * v_k * (15 / v_k))
Step 7: 60 = x - 45
Step 8: x = 60 + 45 = 105.
Wait, let me re-read: 'Another kid runs up the same downward-moving escalator'. If the escalator is moving downward, the kid must climb the 60 steps PLUS the distance the escalator pushes them back.
Step 9: Re-calculating: First kid: 15 steps climbed, 45 steps provided by escalator. Ratio of kid speed to escalator speed is 15:45 or 1:3.
Step 10: Second kid: To cover 60 steps of ground distance while the escalator moves them 45 steps back (since time is the same), they must climb 60 + 45 = 105 steps.
Step 11: Checking options: Option A is 105. Let me double check the 'downward-moving' part. If the escalator is moving down, the kid must overcome the 45 steps the escalator moves down in that time plus the 60 steps of the escalator's length. 60 + 45 = 105.
Step 12: Re-evaluating the prompt's logic. If the first kid climbs 15, the escalator did 45. If the second kid is on a downward escalator, they must cover the 60 steps of the escalator AND the 45 steps the escalator moves down. Total = 105.
Step 13: Wait, the provided options are A: 105, B: 75, C: 90, D: 120. My calculation gives 105. Let me re-read carefully. 'Another kid runs up the same downward-moving escalator'. This implies the escalator changed direction. If the escalator is moving down, the kid must climb 60 + (v_e * t). Since v_e * t = 45, the answer is 105.