# Distance between runners

Tony and Maria are training for a race by running all the way up and down a 700m long ski slope. They each run up the slope at different constant speeds. Coming down the slope, each runs at double his or her uphill speed. Maria reaches the top first, and immediately starts running back down, meeting Tony 70m from the top. When Maria reaches the bottom, how far behind is Tony?

(A)140m (B)250m (C)280m (D)300m (E)320m

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#### Solution Preview

Let Maria's speed be x and 2x for uphill and downhill respectively

Let Tony's speed be y and 2y for uphill and downhill respectively

When they met (time taken was the same)

Time = distance/speed

700/x + 70/2x = 630/y

1470/2x = ...

#### Solution Summary

This is a word problem regarding different speeds. The distances between two runners at a specific point in time are given.