# The hiker, the bicycle and the moped

Alexandra, Bernadette and Cindy all want to go from A to B. The distance is 60 km. (If you prefer miles, simply read miles instead of kilometers in this puzzle.)

They have a bicycle and a moped. Both are without backseat, so only one person can use them at any time.
A hiker walks 5 km/hour.
A Cyclist goes 10 km/hour.
The moped rider makes 20 km/hour.

A hiker would take 60/5=12 hours.
A cyclist would take 60/10=6 hours
The moped rider would take 60/20= 3 hours.
Together that is 12+6+3=21 hours, or 7 hours average.

Is there a way, by alternating transport means, that the three people all can make it in 7 hours?

If you are stuck, one possible solutions is given here. Be aware that more solutions are possible.

This puzzle is based on a similar problem in Pythagoras, issue 1 1967/1968. The distance and the speeds have been changed.

It is easy to see simplify this problem to 2 persons, A and B. The solutions become pretty trivial. But how about expanding the puzzle to 4 people, or 5, or even to n people?

A new puzzle is published every friday. You are welcome to comment on the puzzles. Solutions are usually added after one or more weeks.