A cyclist travels a total distance of 100 kilometers. She cycles x percent of the route at 12 kilometers per hour and the remaining portion at 18 kilometers per hour. In terms of x, where 0 ≤ x ≤ 100, what was the cyclist's speed for the entire trip?

Using the total distance divided by the total time, the average speed is 100 divided by the sum of the times for each segment. The time for the first part is x divided by 12, and the time for the second part is 100 minus x divided by 18. This gives 100 divided by the quantity x over 12 plus the quantity 100 minus x over 18, which equals 3600 divided by the quantity x plus 200.

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