Two cyclists 84 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 4 hours later what is the speed (in miles) of the faster cyclist?
so, if the slower one's speed is x, then together they cover 3x mi/hr
since distance = speed * time,
3x*4 = 84
Speed of slowest cyclist = X mi/h.
Speed of Fastest cyclist = 2x mi/h.
d = 4*x + 4*2x = 84.
4x + 8x = 84,
12x = 84,
X = 7 mi/h.
2x = 14 mi/h.
Well, it looks like we have a classic case of a dynamic bike duo! Let's break it down with a touch of clownish humor.
Let's call the slower cyclist "Turtle" and the faster cyclist "Hare." Now, we know that Hare is twice as fast as Turtle. So it's safe to say that Hare might have consumed a few too many energizing carrots.
Now, since they're 84 miles apart and meet 4 hours later, we can use a simple formula: Distance = Speed × Time.
Let's assume that Turtle's speed is x miles per hour. In that case, Hare's speed will be a zippy 2x miles per hour.
So for Turtle: Distance = Speed × Time gives us 84 = x × 4, leading to x = 21 mph.
And for Hare: Distance = Speed × Time gives us 84 = 2x × 4, which simplifies to 84 = 8x. Solving for x, we find that Hare's speed is 10.5 mph (2 x 21 mph).
So, the speed of our carrot-fueled friend, the Hare, is 10.5 mph! Hop, hop, hop!
Perhaps Hare should slow down a bit to give Turtle a chance to catch up. After all, teamwork makes the dream work!
Let's assume the speed of the slower cyclist is x miles per hour.
Since the faster cyclist cycles 2 times as fast as the slower cyclist, their speed will be 2x miles per hour.
When two objects move towards each other, their combined speed is added up.
In this case, the combined speed of the two cyclists is (x + 2x) = 3x miles per hour.
We know that the distance between them is 84 miles and they meet after 4 hours.
So, the equation to represent this scenario is distance = speed × time.
For the slower cyclist: distance = x miles per hour × 4 hours = 4x miles.
For the faster cyclist: distance = 2x miles per hour × 4 hours = 8x miles.
Since they are cycling towards each other, their individual distances will add up to 84 miles:
4x + 8x = 84.
Combining like terms, we have:
12x = 84.
Dividing both sides by 12, we get:
x = 7.
So, the speed of the slower cyclist is 7 miles per hour.
Since the faster cyclist is cycling 2 times as fast, their speed will be:
2 × 7 = 14 miles per hour.
Therefore, the speed of the faster cyclist is 14 miles per hour.
To solve this problem, we'll use the formula distance = speed × time.
Let's assume the speed of the slower cyclist is x miles per hour. Since the faster cyclist cycles 2 times as fast, their speed would be 2x miles per hour.
We're given that the cyclists are 84 miles apart and are riding towards each other. So, the total distance they have to cover to meet is 84 miles.
Now, let's calculate the time it takes for them to meet. Since they both start at the same time and travel for the same amount of time, we can use the equation: time = distance / speed.
For the slower cyclist: time₁ = 84 / x
For the faster cyclist: time₂ = 84 / (2x)
According to the problem, the total time they took to meet is 4 hours. So, we have the equation: time₁ + time₂ = 4.
Substituting the values we found earlier, the equation becomes:
84 / x + 84 / (2x) = 4
To solve this equation, we can multiply through by 2x to eliminate the denominators:
2(84) + 84 = 4(2x)
168 + 84 = 8x
252 = 8x
Now, we can solve for x by dividing both sides of the equation by 8:
x = 252 / 8
x = 31.5
So, the speed of the slower cyclist is 31.5 miles per hour. Since the faster cyclist goes twice as fast, their speed would be 2 * 31.5 = 63 miles per hour.
Therefore, the speed of the faster cyclist is 63 miles per hour.