Two cyclists, 64 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
Let "x" be the slower rate
the faster rate is "3x"
x+3=2x
64/2=32
2x=32/2
x=16 and 3x=48
This question was marked wrong on my homework and I'm not sure why. please help me
you are mixing up all kinds of unrelated numbers, and then throwing darts at the calculations.
If x is the slower rate, then 3x is the faster rate. So far so good. Now consider that distance = time * speed, and the total distance covered is 64 miles. Since the time for both riders is 2 hours, we have
2*x + 2*3x = 64
8x = 64
x = 8
So, the speeds are 8 mi/hr and 24 mi/hr. In 2 hours, the riders cover 16+48 = 64 miles.
In some bizarre fashion you came up with the distances at the end, but not the speed of the faster rider, which is what they asked for.
To solve this problem, you correctly defined two variables: "x" for the slower cyclist's rate and "3x" for the faster cyclist's rate. However, the equation you set up, "x + 3 = 2x," is incorrect.
Since both cyclists are traveling towards each other, their distances traveled combined should equal the total distance between them. Additionally, it is important to consider the time it takes for both cyclists to meet. They meet after 2 hours, so we need to multiply the rate of each cyclist by the time.
The slower cyclist travels at a rate of "x" miles per hour for 2 hours, so the distance traveled by the slower cyclist is 2x miles.
The faster cyclist travels at a rate of "3x" miles per hour for 2 hours, so the distance traveled by the faster cyclist is 2(3x) = 6x miles.
Since the total distance traveled by both cyclists is 64 miles, you can set up the equation:
2x + 6x = 64
Combining like terms gives you:
8x = 64
Dividing both sides by 8 gives you:
x = 8
Therefore, the slower cyclist's speed is 8 mph, and the faster cyclist's speed is 3 times that, which is 3 * 8 = 24 mph.
To solve this problem, you can set up a distance formula. Let's assume the speed of the slower cyclist is "x" miles per hour. The faster cyclist's speed will then be 3 times that, or "3x" miles per hour.
Since they are 64 miles apart and are moving towards each other, the total distance between them will decrease over time. We can calculate the distance traveled by the slower cyclist in 2 hours as 2x miles, and the distance traveled by the faster cyclist in the same time as 2(3x) = 6x miles.
According to the problem, they meet 2 hours later, so the sum of their distances traveled must equal the initial distance between them. Therefore, we have the equation:
2x + 6x = 64
Combining like terms, we get:
8x = 64
Dividing both sides by 8, we find:
x = 8
So, the speed of the slower cyclist is 8 miles per hour. The speed of the faster cyclist is 3 times that, or 3 * 8 = 24 miles per hour.
Therefore, the correct answer is that the speed of the faster cyclist is 24 mi/h.