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, 2015

Algebra Difficulty 1.1 Junior Find the answer Canada

Six points $P, Q, R, S, T, U$ are equally spaced along a straight path.

Emily walks from $P$ to $U$ and then back to $P$ . At which point has she completed 70% of her walk?

Pick one

Solution

Suppose that the distance between consecutive points on the path is $d$ .

Then, walking from $P$ to $U$ , Emily walks a total distance of $5d$ .

Walking back from $U$ to $P$ , she also walks a distance of $5d$ , for a total distance walked of $10d$ .

Since 70% of 10 is 7, then she has completed 70% of her walk after walking a distance of $7d$ (that is, after having walked 7 segments).

She has walked a distance of $7d$ after walking a distance of $2d$ back from $U$ , which gets her to $S$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.