Two cyclists leave towns 189 kilometers apart at the same time and travel toward each other. One cyclist travels 7 kmh slower than the other. If they meet in 3 hours, what is the rate of each cyclist?
Question
Two cyclists leave towns 189 kilometers apart at the same time and travel toward each other. One cyclist travels 7 kmh slower than the other. If they meet in 3 hours, what is the rate of each cyclist?
Solution
Let's denote the speed of the faster cyclist as x km/h. Therefore, the speed of the slower cyclist is x - 7 km/h.
Since they are traveling towards each other, their combined speed is x + (x - 7) = 2x - 7 km/h.
They meet after 3 hours, so the total distance they covered is the combined speed times the time, which is (2x - 7) * 3.
We know that the total distance between the towns is 189 km, so we can set up the equation:
(2x - 7) * 3 = 189
Solving this equation will give us the speed of the faster cyclist (x), and subtracting 7 from that will give us the speed of the slower cyclist.
Let's solve the equation:
2x * 3 - 7 * 3 = 189 6x - 21 = 189 6x = 189 + 21 6x = 210 x = 210 / 6 x = 35
So, the faster cyclist is traveling at 35 km/h, and the slower cyclist is traveling at 35 - 7 = 28 km/h.
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