Every morning, Tom cycles a set distance at his usual pace (S). One day, he decides to increase his speed by 40% for the first half of his ride and then decrease his speed by 15% for the remaining half of the distance. What's the ratio of the time it takes him to cycle the faster segment compared to the time he spends cycling the slower segment?

Let the usual speed be S and the total distance be 2D, making each half D. His speed for the first half is 1.4S, so the time taken is D divided by 1.4S. His speed for the second half is 0.85S, so the time taken is D divided by 0.85S. The ratio of the time spent on the faster segment to the time spent on the slower segment is (D / 1.4S) divided by (D / 0.85S), which simplifies to 0.85 divided by 1.4. Multiplying the numerator and denominator by 100 gives 85 to 140, which simplifies to a ratio of 17 : 20.

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