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Riddle of the week: bike tour with obstacles


Eva and Lukas want to do a 40-kilometer tour - but only have one bike. So they alternate with running and driving. How fast are the two at the finish?

40 kilometers are long if you have to walk the route. Eva and Lukas want to do the trip with bicycles. They can average 20 km / h on the flat track and have to be there after two hours.

As they are about to leave, Eva realizes that the chain of her bike has broken. Without tools, the two can not repair the mishap. So you only have one bike on which unfortunately no second person can ride.

Eva has an idea: "We alternate with cycling."

"How is that supposed to work?" Asks Lukas.

"One is running, one is riding the bike," explains Eva. "I start on the bike and drive in. If I have driven a few kilometers, I get off the bike, leave it on the side of the road and continue on foot towards the finish."

"And what happens to the bike?" Asks Lukas.

You're following me on foot all the time, you get on the bike and ride until you catch up with me again, so I'll go ahead. "

"And then everything starts all over again?"

"Exactly," says Eva. "I'll take the bike again and drive ahead until I finally leave the bike for you and continue on foot, and so on."


What is the shortest possible time for Eva and Lukas to reach their destination 40 kilometers away? The running speed is 5 km / h on both, on the bike they reach 20 km / h.

Source: spiegel

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