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Q16. The speed limit on a road is 40mph. A scooter drives 9 miles in 13 minutes. Is the scooter breaking the speed limit? |
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Answer» ong>Step-by-step explanation: Yes: we’re comparing 9/13 miles per MINUTE to the limit of 40/60=2/3 miles per minute. Multiply both by 13*3; now we’re asking if 9*3 is larger than 2*13. The answer is yes: 27>26. So we’re breaking the speed limit. If you want to avoid calculation, you can alternatively rewrite 2/3 miles per minute as 8/12 miles per minute. Now both SPEEDS are PART of the sequence 1/4, 2/5, 3/6, 4/7, 5/8, 6/9, … Note that this sequence is monotonically increasing (SINCE the derivative of X/(x+4) is positive, if you want a proof), so 9/13 is larger than 8/12. In general, for 0≤p |
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