3. Barbara is at the railway station and reports to her mother: "The train arrived 10 minutes ago, and we traveled exactly four hours and twenty-two minutes!" At that moment, her mother looked at the clock, and it showed 13 h and 5 min.

a) At what time did the train Barbara arrived on depart?

b) What type of angle did the clock hands form at the time of the train's departure?
3. a) At 13 h and 5 min, Majka looked at the clock, and since Barbara arrived 10 minutes earlier, it means she arrived at the station at 12 h and $55 \mathrm{~min}$. 1 POINT

Since she traveled for four hours and twenty-two minutes, we have:

$12-4=8$ and $55-22=33$

b) Sketch:

![](https://cdn.mathpix.com/cropped/2024_05_30_f994d10c66c436712f92g-4.jpg?height=565&width=540&top_left_y=543&top_left_x=290)

At 8 h and 33 min, the clock hands formed an acute angle.

Note: The solution could also be a reflex angle. The sketch should be awarded 1 POINT, as well as the conclusion that the clock hands form a reflex angle.

![](https://cdn.mathpix.com/cropped/2024_05_30_f994d10c66c436712f92g-4.jpg?height=574&width=557&top_left_y=1335&top_left_x=287)