Unitary method

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The unitary method is a technique in elementary algebra for solving a class of problems in variation. It consists of altering one of the variables to a single unit, i.e. 1, and then performing the operation necessary to alter it to the desired value.

For example, to solve the problem. 'A man walks seven miles in two hours. What is his average speed?', we aim to calculate how far the man walks in one hour. We can safely assume that he would walk half the distance in half the time. In one hour (one half of two hours) he walks three and a half miles (one half of seven miles). His speed is therefore three and a half miles per hour.

We can apply the same method to the problem 'A man walks at four miles per hour. How long would it take him to cover five miles?' by asking first, how long does the man take to walk one mile. One is a quarter of four, so it takes him a quarter of an hour to walk one mile. To walk five miles it therefore takes him five quarter hours, or an hour and a quarter.

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