Problem 4 · 1997 AJHSME
Medium
Ratios, Rates & Proportions
unit-raterange-check
Julie is preparing a speech. It must last between one-half hour and three-quarters of an hour, and her ideal rate is 150 words per minute. If she speaks at that rate, which of the following word counts is an appropriate length?
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Answer: E — 5650 words.
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Hint 1 of 2
A 'between' problem becomes easy once you turn the two time limits into the language of the answer — word counts. Convert the fences, then see which choice sits inside.
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Hint 2 of 2
When a quantity must fall in a range, translate BOTH endpoints into the same units as the answers and look for the one trapped between them.
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Approach: convert the time fences to word counts, then trap the answer
- Half an hour = 30 min, three-quarters = 45 min. At 150 words/min the speech must hold between 150 × 30 = 4500 and 150 × 45 = 6750 words.
- Scan the choices for the one inside [4500, 6750]: 2250, 3000, 4200 are too low; 4350 is still under 4500; only 5650 fits.
- Sanity check: 5650 ÷ 150 ≈ 37.7 minutes — comfortably between 30 and 45, confirming it.
- You'll see it again: for 'which value is in the allowed range' questions, compute the two boundaries first; you rarely need to test every answer.
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