Two cyclists start at the same point and travel in opposite directions. One cyclist travels 6 kmh slower than the other. If the two cyclists are 92 kilometers apart after 2 hours, what is the rate of each cyclist?
Question
Two cyclists start at the same point and travel in opposite directions. One cyclist travels 6 kmh slower than the other. If the two cyclists are 92 kilometers apart after 2 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 would be x - 6 km/h.
Since they are traveling in opposite directions, their speeds are added together. So, their combined speed is x + (x - 6) km/h.
They are 92 kilometers apart after 2 hours, so their combined speed is 92 km / 2 hours = 46 km/h.
Setting this equal to the expression for their combined speed gives us the equation:
x + (x - 6) = 46
Solving this equation will give us the speed of each cyclist.
Step 1: Combine like terms on the left side of the equation:
2x - 6 = 46
Step 2: Add 6 to both sides of the equation to isolate the term with x:
2x = 52
Step 3: Divide both sides of the equation by 2 to solve for x:
x = 26
So, the faster cyclist is traveling at 26 km/h, and the slower cyclist is traveling at 26 - 6 = 20 km/h.
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