## Teaser 2940: Getting there in the end

**From The Sunday Times, 27th January 2019** [link]

A tractor is ploughing a furrow in a straight line. It starts from rest and accelerates at a constant rate, taking a two-digit number of minutes to reach its maximum speed of a two-digit number of metres per minute. It has, so far, covered a three-digit number of metres. It now maintains that maximum speed for a further single-digit number of minutes and covers a further two-digit number of metres. It then decelerates to rest at the same rate as the acceleration. I have thus far mentioned ten digits and all of them are different.

What is the total distance covered?

As stated this puzzle does not have a unique solution.

[teaser2940]

## Jim Randell 7:12 am

on3 March 2019 Permalink |The tractor starts at rest:

It then accelerates, at constant rate

a, in timet1, to velocityv:During this period it has covered a distance

d1:It continues at a constant velocity

v, for timet2, and covers distanced2:It then decelerates to rest, at a rate of

–a, covering distanced1again.The required answer being:

We can consider the alphametic expressions where:

This can be easily solved by the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary.This run-file executes in 126ms.

Run:[ @repl.it ]Solution:There are three possible total distances: 646m, 864m, 1316m.None of the solutions are particularly realistic. Each of them involve the tractor accelerating incredibly slowly for a very long time to reach an extremely modest top speed, and later take just as long to decelerate. Perhaps with a change of units the problem could made to apply to something that does take a long time to decelerate, like a train, oil tanker or spaceship.

It would also have been easy to require just one of the possible answers, maybe by specifying the answer has 4 digits (1316m), or that all the digits are different (864m).

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