Subject: geometry(rewriting and evaluating formulas grade 12)

I am a parent and need some help.

This is the question.

Due to the wide range of temperatures experienced in Canada, engineers who construct roads must allow for expansion and contraction of the road surface. The following formula is used to calculate the amount of expansion E to allow for: E= kL(T-t), where k is the constant of expansion for the road surface. L is the length of the section of highway in metres. T is the temperature of the air in degrees Celsius. t is the temperature, in degress Celsius, at which the section of the highway was constructed.

If a 3000m section of highway is built when the temperature is 22 C, find the expansion that will occur on a day when the temperature reaches 28 C. The constant of expansion for the road surface is 0.000 027.

could you please help me, and explain how you arrived at your answer.

Thank you,

A conserned mother.


Actually, this has only the illusion of being geometry - it is really just rewriting/plugging in to formulas, with information someone may have extracted from geometry and physics.

You have a formula, and a paragraph trying to give you the values for each of the letters (except the one answer you are looking for) which appear in the formula.

It is now a matter of replacing letters by corresponding numbers and then seeing which calculations (multiplications, subtractions etc.) you need to do with the numbers.

So, for example, L = 3000m (meters). You did not give any units for the coefficient of expansion, so I would suspect it is per degree Celsius (to make the physics units work out and E to be measured in meters m).

I am not sure what else to say that would not simply compute the answer (something the student needs to practice).

Walter Whiteley
York University

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