Two cyclists, 128 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other. If they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?
they close the distance at 32 mph (128/4)
x + x/3 = 4x / 3 = 32 mph
Wrong. It can't be 32miles per hour as x 4 hrs that is the full 128 miles. What happened to the slower cyclist?
Distance = speed x time
Let s stand for cylcist 1 speed. Therefore cyclist 2 speed must be 3s.
The equation then looks like this
128 = 4s x 4
128 = 16s
8 = s
so the speed of the slower cyclist is 8 m/h and since cylist two is 3x as fast his speed must be 24m/h.
test:
1) 4 hrs x 8 miles = 32 miles
2) 4 hrs x 24 miles = 96 miles
96 + 32 = 128 miles.
128 = 4s x 4
Well, that's quite a biking buddy comedy! Let's break it down.
Let's call the speed of the slower cyclist "x" miles per hour. Since the faster cyclist is three times as fast, we can call their speed "3x" miles per hour.
Now, both cyclists are riding for 4 hours, and the combined distance they cover is 128 miles. Since distance equals speed multiplied by time, we can write an equation:
Distance of slower cyclist + Distance of faster cyclist = 128 miles
So, we have the equation:
4x + 4(3x) = 128
Simplifying that, we get:
4x + 12x = 128
16x = 128
Dividing both sides by 16, we find:
x = 8
Since the faster cyclist's speed is 3 times that of the slower cyclist, their speed is:
3 * 8 = 24 miles per hour!
So, the faster cyclist is pedaling at a clownishly fast speed of 24 miles per hour. Watch out for those speedy cyclists on the road!
Let's assume the speed of the slower cyclist is x miles per hour.
According to the given information, the speed of the faster cyclist is 3x miles per hour because they cycle 3 times as fast.
When two objects are moving towards each other, their total distance covered is equal to the sum of their individual distances.
The slower cyclist travels at a speed of x miles per hour for 4 hours, so their distance covered is 4x miles.
Similarly, the faster cyclist travels at a speed of 3x miles per hour for 4 hours, so their distance covered is 4(3x) = 12x miles.
Since the total distance covered by both cyclists is 128 miles, we can write the equation:
4x + 12x = 128
Simplifying the equation:
16x = 128
Dividing both sides by 16:
x = 8
Therefore, the speed of the slower cyclist is 8 miles per hour.
Since the speed of the faster cyclist is 3 times the speed of the slower cyclist, the speed of the faster cyclist is 3 * 8 = 24 miles per hour.
So, the speed of the faster cyclist is 24 miles per hour.
To find the speed of the faster cyclist, we need to set up an equation using the information given.
Let's assume the speed of the slower cyclist is 'x' miles per hour. Since the faster cyclist cycles 3 times as fast, their speed will be '3x' miles per hour.
When two objects are moving towards each other, their relative speed is the sum of their individual speeds. Therefore, the combined speed of the two cyclists is 'x + 3x = 4x' miles per hour.
Now, we can use the equation distance = speed * time to find the total distance covered by both cyclists. The combined distance covered by both cyclists is 128 miles, and they meet after 4 hours, so the equation is:
4x * 4 = 128
Now we can solve this equation to find the value of 'x':
16x = 128
Dividing both sides of the equation by 16, we get:
x = 8
Therefore, the speed of the slower cyclist is 8 miles per hour.
Since the faster cyclist cycles 3 times as fast, their speed is:
3 * 8 = 24 miles per hour.
Hence, the speed of the faster cyclist is 24 miles per hour.