Mario lives in Brooklyn, New York. He has two married brothers, Luigi and Bob, who lived in Schenectady and Buffalo. Every Saturday Mario, who is single, would take an Uber to Grand Central Station in New York City and catch a train to see one of them. To save money, he used the ride share option where the Uber driver could pick up one to three additional passengers to take to the same train station.

Sometimes Mario was the only passenger and the commute was quick. Sometimes the car carried with four passengers plus the driver so the trip took longer. Thus ride share resulted in different arrival times at the train station.

Mario had never met most of the extra riders he shared the Uber with. But that was okay with him because trains left for Schenectady and Buffalo every twelve minutes. He left it up to chance which brother he would visit. When he arrived at the train station, he bought a ticket for whichever train left next.  

After a year, brother Bob asked Mario why he visited his brother Luigi about five times as often as he did Bob… 

Bob was right. And this week’s Micro Softy’s challenge is to figure out why.

Solution to Micro Softy 45:  Tony and the fast-food curfew

Last week’s Micro Softy is a classic story problem. Tony bicycled to Burger Doodle at 12 miles an hour and home at 6 miles per hour. What was his average speed for the round trip?

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His average speed is independent of the distance to the store. So let’s say the distance to the store is 12 miles one way. Going to the store at 12 miles an hour, Tony took one hour. Coming back at half the speed, it took twice as long – 2 hours. Therefore, Fat Tony covered 24 miles in three hours. His average speed was therefore 24 miles/3 hours = 8 miles per hour.

If you are troubled by the assumption that the average velocity is independent of D = distance to the store, here’s some more general math: Since distance is equal to velocity × time, the time it takes to go to the store at 12 miles per hour is T1=D/12 hours. The time to return home at 6 miles per hour is T2=D/6 hours. The total round-trip time is T=T1+T2. The distance for the round trip is 2D so the average speed is Vavg = 2D/T = 8 miles per hour – the same answer as before.

The Monday Micro Softy is a weekly feature of Mind Matters News. Here are the links to all the puzzles and answers to date:

Monday Micro Softy 45: Can Tony beat the fast-food curfew? An early curfew on fast food service motivated a boy to exercise more vigorously. But how fast was he pedaling? To solve Micro Softy 44, recall that Tony doesn’t need to take the individual pills each day, only the prescribed amount of each.You will find links here to Micros Softies 41 through 44 as well.

Monday Micro Softy 40: The fate of a false prophet. He wasn’t actually fired for being a false prophet but for something that his prophecy unintentionally revealed. The solution to Micro Softy 39 lies in considering an alternative possible meaning of a word commonly used in sports. You will also find links to Micro Softies 30 through 39 and their answers here as well.

Monday Micro Softy 29: A funeral lament in four lines. The funeral director was puzzled by Dan’s description of his relationship to the deceased but there was no question that his grief was sincere Here, you will also find links to Microsofties 22 through 29.

Monday Micro Softy 21: Finding More of the Deadly Fentanyl Pills. Here, you will also find links to Microsofties 11 through 20 as well.

Monday Micro Softy 11: What Happened to That Other Dollar? Here you will find links to the first ten Micro Softies. Have fun!