John would have reduced the time it took him to drive from his home to a certain store by 1/3 if he had increased his average speed by 15 miles per hour

题目

John would have reduced the time it took him to drive from his home to a certain store by 1/3 if he had increased his average speed by 15 miles per hour. What was John's actual average speed, in miles per hour, when he drove from his home to the store?

选项

解析

我们先列出文字等式：约翰以更快速度的行驶时间 = \(\frac{2}{3}\) × 约翰的常规行驶时间设 \(r =\) 约翰的常规速度因此，\(r+15 =\) 约翰的更快速度设 \(d =\) 以常规速度行驶的距离因此，\(d =\) 以更快速度行驶的距离时间 = 路程 ÷ 速度因此我们得到：\(\frac{d}{r + 15} = \frac{2}{3} \times \frac{d}{r}\) 改写为：\(\frac{d}{r + 15} = \frac{2d}{3r}\) 交叉相乘：(d)(3r) = 2d(r + 15) 展开：3rd = 2rd + 30d 整理得：rd = 30d 两边同时除以\(d\)，得：r = 30 答案：B

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