Problem 7 · 2022 AMC 8
Easy
Ratios, Rates & Proportions
distance-speed-timeunit-rate
When the World Wide Web first became popular in the 1990s, download speeds reached a maximum of about 56 kilobits per second. Approximately how many minutes would the download of a 4.2-megabyte song have taken at that speed? (Note that there are 8000 kilobits in a megabyte.)
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Answer: B — 10 minutes.
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Hint 1 of 2
The speed is in kilobits per second but the song is in megabytes — the units don't match. Fix that first; everything else is one division.
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Hint 2 of 2
Convert the song to kilobits (4.2 × 8000), then time = size ÷ speed, and finish by turning seconds into minutes.
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Approach: make the units match the speed, then divide
- Insight: don't divide yet — the answer choices span 0.6 to 36000, so a units slip is the whole danger. The speed is in kilobits/sec, so put the song in kilobits too: 4.2 × 8000 = 33,600 kilobits.
- Time = 33,600 ÷ 56 = 600 seconds = 10 minutes.
- Lighter path: avoid the big division by reshaping the size as 56 × (something): 33,600 = 56 × 600, so it's 600 seconds straight off — then ÷60 for minutes.
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