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  3. When a certain stretch of highway was rebuilt and straightened，the distance alon

When a certain stretch of highway was rebuilt and straightened，the distance alon

游客2024-01-13  29
问题 When a certain stretch of highway was rebuilt and straightened，the distance along the stretch was decreased by 20 percent and the speed limit was increased by 25 percent．By what percent was the driving time along this stretch reduced for a person who always drives at the speed limit?
选项 A、 
B、 
C、 
D、 
E、 
答案 B
解析 Let D and r be the distance and speed limit, respectively, along the stretch of highway before it was rebuilt. Then, the distance and speed limit along the stretch of highway after it was rebuilt are given by 0.8D and 1.25r. It follows that the percent reduction in time is

Alternatively, it helps to use actual numbers when calculating percent change, with 100 being the most mathematically convenient number to use. For this problem, set the speed limit at 100 miles per hour and the distance at 100 miles.
A 20 percent decrease in distance makes the new distance 80 miles. A 25 percent increase in speed limit makes the new speed limit 125 miles per hour, which, of course, is unrealistic, but very convenient to work with. Then, the new time distance/rate is 80/125 hours, The percent change in time is
The correct answer is B.
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