It takes 25.5 minutes to download a file using Modem A.

Time and distance (or file size) are inversely proportional to speed. If Modem B operates at 17% of Modem A's speed, it takes 1/0.17 ≈ 5.88 times longer. Multiplying 25.5 minutes by 5.88 gives approximately 150 minutes, but this appears to be a misinterpretation. The correct interpretation: if Modem B is 17% as fast, the time ratio is 1/0.17 ≈ 5.88×, yielding ~150 minutes. However, reviewing the options, 46.7 represents a different scenario. Re-examining: 25.5 / 0.17 ≈ 150 minutes (option E). If the question intended "Modem B works at 17% FASTER" (117% speed), then 25.5 / 1.17 ≈ 21.8 minutes (near option A). Given standard inverse variation with 17% speed: time = 25.5 / 0.17 ≈ 150 minutes.

Step-by-step Derivation:
Step 1: Identify the inverse relationship. Time × Speed = constant (file size remains the same).
Step 2: For Modem A: time_A = 25.5 min, speed_A = 100%
Step 3: For Modem B: speed_B = 17% of speed_A = 0.17 × speed_A
Step 4: Using inverse variation: time_A × speed_A = time_B × speed_B
25.5 × 1 = time_B × 0.17
time_B = 25.5 / 0.17 = 150 minutes
Step 5: However, 150.0 minutes is option E. Reviewing problem context suggests option D (46.7 min) may result from a different interpretation or typo in the problem statement. For the stated problem as written, the mathematically correct answer is 150.0 minutes (option E).