This year Formula One teams that agree to race within a strict budget rather than relying on unlimited funds to develop their cars are being rewarded with a number of perks under a scheme called the Kinetic Energy Recovery System. And one of the bonuses includes a booster button that can be pushed for a maximum of 6.7 seconds during a race.

This has led to some interesting mathematical questions. If you are behind the wheel of a Formula One car and you have this booster button, when is the best time to press it and release the power? Should you do it to help overtaking, or should you use it to get through a slower section of the course?

The designers of Formula One cars already rely on a huge amount of mathematical input. But the question of optimising the use of such a button is the perfect opportunity for the mathematician to take the driving seat.

Indeed, a similar question has been exercising minds on the blog of one of the world’s leading mathematicians. Terence Tao won a Fields medal, the mathematician’s Nobel prize, in the latest round of awards along with Grigori Perelman, the Russian recluse who solved the Poincaré Conjecture. Although Perelman turned his down, Tao has been revelling in the limelight and writes a popular blog (among maths geeks anyway), discussing a range of complex mathematics from partial differential equations to low-dimensional topology.

But a recent discussion concerned a more mundane problem that turned out to be close to the heart of the globe-trotting mathematicians as they jet between international conferences.

You arrive at an airport for a flight connection but the timing is tight. You discover that your next plane is leaving from the far end of the airport. There is a moving walkway for part of the journey. You’ve got enough energy to do a short burst of running, but otherwise you’ll walk at a constant speed. However, one of your shoelaces is undone so you’re going to need to stop at some point to do it up.

You want to get to the gate as quickly as possible, so the question is: when should you use your burst of energy? Should you run on or off the moving walkway? And that shoelace? Should you tie that on the moving walkway? Or should you stop on the portion of the journey without a moving walkway? Or does it make no difference where you run or stop?

A mathematician’s instinct is to reach for algebra to unravel the problem, and that is a sure way of getting the right answer. But sometimes a little lateral thinking can save you the ink. One blogger had twins setting off simultaneously. As they approached the moving walkway one twin stopped to do up his lace, the other stepped on and did his lace on the moving walkway. It is clear that by the time both have finished tying their lace, the twin who tied on the walkway is well ahead of his brother. So shoelaces should be tied on the walkway.

But what about the burst of running? Our twins are walking together towards the walkway when one twin decides to press the boost button to get him to the walkway before his brother. He reaches it D metres ahead of his brother. But as soon as he steps on to the walkway the distance between them begins to increase even more. When the second twin steps on to the walkway he presses his booster. Since both are on the walkway, this will allow him to catch up only D metres on his brother. But his brother is more than D metres away by now. So the boost button should be hit off the runway.

There is an economic maxim that underlies both decisions: a worker should spend as much time as possible on the most efficient machine. In this case, staying on the walkway for as long as possible is the best strategy. Stop to tie the shoelace on the walkway but don’t press the boost button as it will get you off the walkway quicker. Save that for the bit of the airport without the moving walkway.

Of course, if you wait until you reach the walkway before you tie your lace, you may discover one disadvantage — tripping flat on your face! So, while Formula One teams would be well advised to monitor the blogs of the world’s leading mathematicians, they should also bear in mind good old-fashioned common sense.

Conundrum

A biker travels to work at 30 miles per hour. Coming home, the roads are clearer so he travels 45mph. What is his average speed?

Answer

36mph (not 37.5mph). Suppose the distance from home to work is 45 miles. It takes 1.5 hours in the morning and 1 hour on the way home. So the average speed is (45+45) ÷ 2.5 = 36mph.

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