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Mathematics Tip – Conversion Between Units of Measure

Yesterday we explained about units of measurement. In this article , you can check what they are, what the importance is, what is the International Measurement System (SI) and some tips on using magnitudes in the National High School Examination (Enem) questions.

We also show that when the statement of a question brings a magnitude with a particular unit but asks for the answer in another unit, it is necessary to perform the conversion between the units of measurement.

To illustrate this, we bring up today a question of the Enem 2014 of the Mathematics and Its Technologies book that was solved and commented by the professors Luís Gustavo and Ana Luísa, graduated in Mathematics by UNICAMP and responsible for solving all Mathematical issues of our material.

Enem 2014 – Issue 168 – Pink Notebook

The Traffic Engineering Company (CET) of São Paulo tested in 2013 new radars that allow the calculation of the average speed developed by a vehicle on a stretch of track.

Measures

Speed measurements would no longer occur instantaneously when passing through the radar, and would be made from the average speed in the stretch, considering the time spent on the route between one radar and another. It is known that the average speed is calculated as the ratio of the distance traveled and the time spent traveling through it.

The test performed showed that the time allowed for safe driving of the displacement between the two radars should be at least 1 minute and 24 seconds. With this, the CET needs to install a plate before the first radar informing the maximum average speed allowed on that stretch of track. The value to be displayed on the plate should be as large as possible, among those that meet the safe driving conditions observed.

Available at: www1.folha.uol.com.br. Accessed on: 11 Jan. 2014 (adapted).

The signaling plate that informs the speed that meets these conditions is

alternatives

 

RESOLUTION AND COMMENTS

Alternative C

The first fundamental idea in this question is the incompatibility between the units. We should give the answer in km / h, but the time we get is in minutes and seconds. Therefore, the first step to be performed is unit conversion:

Measures1

Since 1 hour has 3 600 seconds, we can make a rule of three to get how many hours equals 84 seconds:

Measures2

The second fundamental idea is to use this value, which is the minimum time established for safe driving between the radars on the track, to find out what the maximum allowed speed will meet the conditions imposed. The statement provided how to calculate the average speed that is the ratio between the distance traveled and the time spent to traverse it. As the distance between the radars is 2.1 km, the calculation of the average speed will be:

Measures3

Comentário: A questão envolveu o cálculo da velocidade média, um conceito da Física, porém o enunciado trouxe como calculá–la. Ao aluno coube a habilidade em receber uma informação e utilizá–la para resolver o que foi pedido. Note que durante a resolução não efetuamos a primeira divisão (84 ÷ 3 600) o que tornou a segunda divisão menos trabalhosa, pois foi possível simplificar a fração dividindo o numerador e o denominador por 21.

Conteúdo envolvido: Conversão de unidade e velocidade média.