There are scheduled buses traveling between Somewhere and Nowhere. There is only one road between the two villages, so the buses take this road. From both villages the buses leave for the other village at every hour and at every half an hour, and travel with the same speed for the whole trip. If there is no traffic jam, the buses leaving the villages at the same time meet on the road between the two villages 10 minutes later. One month, however, there was a construction on the road, and the buses (on the days when the workers were working) had to wait 5 minutes at the border of the village from which they just left. Other than that, the buses traveled the same way as before. (The workers did not work every day.) During the 30 days of the road construction the buses met in an average 14 minutes after leaving. How many days out of the 30 did the workers work?
2026-04-17 20:09:31.1776456571
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how many days at work?
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Since the buses are "waiting" for five minutes at the start (assuming village borders are pretty close to the start) now, they would travel for a total of 25 minutes, the buses should be expected to meet after 15 minutes since both are waiting at the start.
Since the average is 14 minutes, workers worked on 80% i.e. $\dfrac{14-10}{15-10}$ days in a $30$ day month they must have worked for $24$ days
Hint: On a work day, how many minutes after leaving do the buses meet? You have to average a certain fraction of that with (1-the certain fraction) of 10 and get 14.