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Algebra Difficulty 3.5 AMC 10/12 Find the answer South Africa

Boris takes a taxi to his home but falls asleep when the taxi is halfway to his house. He wakes up when the remaining part of his journey is equal to half the distance covered by the taxi while he was asleep.
If the fraction of the journey for which he slept is 1n\frac{1}{n}, what is the value of nn?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

3 Assume that the remaining distance home is 1 unit. Then he slept for 2 units. Hence, the whole journey is 6 units and the fraction of the ride that he slept for is 26=13\frac{2}{6} = \frac{1}{3}.

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