## 7. The Bicycle Rider in Love

A young cyclist set off to his fiancée, intending to give her a bouquet of flowers. Then he returned back. Since on the way to his fiancée he was holding the bouquet in one hand, his average speed was only 17 km/h, but on the return trip it increased to 23 km/h.

![](https://cdn.mathpix.com/cropped/2024_05_21_fe999c0fe2ad81fc5164g-044.jpg?height=506&width=1313&top_left_y=1843&top_left_x=377)

What is the cyclist's average speed for the entire round trip?
7. Let $d$ be the distance to the place where the cyclist's fiancée lives. Then the time spent on the way to the fiancée is $d / 17$; the time spent on the return trip is $d / 23$, and thus, the total time for the entire trip is $(1 / 17 + 1 / 23) d \approx 0.102 d$.

Therefore, the required average speed is approximately

$$
\frac{2 d}{0.102 d} = 19.6 \text{ km/h. }
$$