Two cyclists, 36 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
Both riders ride for 2 hours
add up their distances to be 36
distance = speed*time
2s + 2*2s = 36
6s=36
s=6
slow rider rides 2hrs*6mph = 12 mi
fast rider rides 2hrs*12mph = 24mi
Well, it seems like we have a race on our hands! Let's call the speed of the slower cyclist "x" miles per hour. That means the speed of the faster cyclist is 2x miles per hour, twice as fast, twice the fun!
Now, in 2 hours, the slower cyclist will have covered a distance of 2x miles, while the faster cyclist will have covered a distance of 4x miles, because 2 times 2 is 4. Alright, math time!
Since they're riding towards each other, the combined distance they have covered is 36 miles. So we can set up an equation: 2x + 4x = 36. Adding those x's like it's nobody's business, we get 6x = 36. Divide both sides by 6, and voila, x = 6.
So, the speed of the slower cyclist is 6 miles per hour, which means the faster cyclist is going at double the speed, a whopping 2 times 6, which is 12 miles per hour! Catching some serious speed there, my friend.
Let's assume the speed of the slower cyclist as 'x' mi/h.
The speed of the faster cyclist will be 2x mi/h (since the faster cyclist's speed is 2 times that of the slower cyclist).
The combined speed of the two cyclists is x + 2x = 3x mi/h.
In 2 hours, they travel a distance of 2 * 3x = 6x miles (since distance = speed * time).
Given that they are already 36 miles apart, the total distance they cover will be 36 miles + 6x miles.
Since they meet at this total distance, we can set up the equation:
36 miles + 6x miles = total distance
Since they meet after riding for 2 hours, the total distance covered by them is simply the sum of the distances covered by each cyclist independently.
Accordingly, we set up the equation:
2x miles/hour * 2 hours + x miles/hour * 2 hours = 36 miles + 6x miles
Simplifying the equation, we get:
4x + 2x = 36 + 6x
Combining like terms, we get:
6x = 36 + 6x
Subtracting 6x from both sides, we get:
0 = 36
This equation is not possible, which means there is an error in either the problem statement or the calculation.
Please recheck the question or the given information, and let me know if you have any other questions.
To solve this problem, we can use the formula: speed = distance/time.
Let's assume the speed of the slower cyclist is x miles per hour. Therefore, the speed of the faster cyclist is 2x miles per hour, as mentioned in the problem.
We know that the distance between them is 36 miles, and they ride towards each other for 2 hours until they meet.
The distance covered by the slower cyclist in 2 hours is speed * time = x * 2 = 2x miles.
The distance covered by the faster cyclist in 2 hours is speed * time = 2x * 2 = 4x miles.
The sum of the distances covered by both cyclists should equal the total distance of 36 miles when they meet. So, we can write the equation: 2x + 4x = 36.
Combining like terms, we get 6x = 36.
Dividing both sides of the equation by 6, we find x = 6.
Therefore, the speed of the slower cyclist is 6 miles per hour, and the speed of the faster cyclist is 2 * 6 = 12 miles per hour.
Hence, the speed of the faster cyclist is 12 miles per hour.