Corona Letters #26 - The Walker, the Biker, and the Small Mathematician

There was a walker walking one way.

There was a biker biking the other way.

They were both on the correct side of the street.

Which was the same side.

Because bikers bike with traffic and walkers walk against traffic.

When they came within six feet of each other they stopped.   The CDC said they could come no closer to each other.

They stared at each other.

There was no shoulder for either of them to let the other pass.

"You are in my way," said the biker.

"You are in my way," said the walker.

"You should cross to the other side of the street," said the biker.

"You should cross to the other side of the street," said the walker.

"My bike is more unwieldy,"  said the biker.

"I would have to take more steps than you would have to pedal," said the walker.

"I would be biking on the wrong side of the street if I crossed," said the biker

"I would be walking on the wrong side of the street if I crossed," said the walker.

They found themselves at an impasse.  Neither of them was willing to budge.  And neither was willing to compromise their health by passing at each other with less than six feet between them.

A small mathematician, on a break from 4th grade home schooling, was watching from the window.
He pondered the dilemma and did some quick calculations on the white board his mother had set up when she was feeling like a productive home school mother/teacher.   Currently, she was in the bathtub with a glass of wine ignoring the small mathematician.

After a bit of agonizing he came up with a solution.

The walker and biker were still at an impasse, both unwilling to move.

The small mathematician ran outside with the white board.  "I've got it!" he yelled.

"Stay Back!" the biker and the walker yelled as the boy came dangerously close to the six foot invisible radius.

The small mathematician came to an abrupt halt.

"I know how you two can pass and neither of you will have to be on the wrong side of the road." said the small mathematician.

The biker and the walker were intrigued.

"I've written out all the calculations here and propose there is one best solution."

The biker and the walker looked at the white board at all the fractions, circles, radii and algebraic equations and told the small mathematician "that is quite advanced for such a small boy."

"I have a lot of time on my hands" said the small mathematician.
Then he continued.   "According to my calculations if the walker, crosses the street and walks ten paces in the opposite direction he was going, he will be obeying traffic laws for pedestrians and then the biker can continue on this side of the street and he will quickly pass the point where the walker will cross back over and continue on his way he was originally walking."

"Well, that's not fair!" said the walker, stomping his foot. "Why should I have to cross? Why can't he?"

"Well," said the small mathematician, "You will see from my calculations here that since the speed of the biker is faster than the speed of the walker, if the biker crosses and goes back in the opposite direction he was going, at the same speed, the walker would never pass him and he could not cross back."

The biker and walker looked at each other, looked at the small mathematician and all nodded in agreement.

So, the walker crossed the street, went ten paces in the opposite direction he had been going and then crossed back and continued on his delightful walk.

The biker happily biked in the same direction in which he had originally been traveling with no need to cross the street or come within six feet of anyone.

The small mathematician went inside and told his mother, who had emerged from the bathroom in her Terry cloth bathrobe with butterflies on it that he was done with math for the day.

He retired to his room.

His mother looked at his white board and said, "Wow.  I'm doing an amazing job at home schooling this kid!"

And that is the story of the walker, the biker, and the small mathematician.