Kathy and Cheryl are walking and running in a fundraiser. Kathy completes the course in 6 hours and Cheryl completes the course in nine hours. Kathy went on average two miles per hour faster than Cheryl. Find Kathy and Cheryl's speed.
distance = speed * time, so we have
k = c+2
6k = 9(k-2)
3k = 18
k = 6
check:
6*6 = 4*9
To find Kathy and Cheryl's speed, we need to determine the distance they each traveled. Since we know the time it took for each of them to complete the course, we can use the formula:
Speed = Distance/Time
Let's first find the distance each person traveled.
Kathy's time is 6 hours, and let's denote her speed as x miles per hour. Therefore, Kathy traveled a distance of 6x miles.
Cheryl's time is 9 hours, and we know that Kathy's average speed was two miles per hour faster than Cheryl's. So, Cheryl's speed would be x - 2 miles per hour. Thus, Cheryl traveled a distance of 9(x - 2) miles.
Since both distances are the same (since they completed the same course), we can set up an equation:
6x = 9(x - 2)
Now, let's solve this equation to find the value of x, which represents Kathy's speed.
To find Kathy and Cheryl's speeds, we'll use the formula: speed = distance / time.
Let's say Kathy's speed is x miles per hour. Since Kathy completes the course in 6 hours, her distance covered will be 6x miles.
Similarly, let's say Cheryl's speed is y miles per hour. Since Cheryl completes the course in 9 hours, her distance covered will be 9y miles.
We're given that Kathy's speed is 2 miles per hour faster than Cheryl's speed, so we can write an equation as follows:
x = y + 2
Now, let's substitute the distances and times into the speed formula for Kathy and Cheryl:
Kathy's speed: x = 6x / 6
Cheryl's speed: y = 9y / 9
Since their respective distances equal the distances covered, we can write:
6x = 6x -- Equation 1
9y = 9y -- Equation 2
Now, let's solve Equation 1 for x:
6x = 6x
6x - 6x = 0
0 = 0
Since 0 = 0, Equation 1 is true.
Next, let's solve Equation 2 for y:
9y = 9y
9y - 9y = 0
0 = 0
Since 0 = 0, Equation 2 is also true.
Since both equations yield 0 = 0, it implies that these equations do not provide any information to determine the value of x (Kathy's speed) and y (Cheryl's speed).
Therefore, we cannot determine the exact values of Kathy and Cheryl's speeds based on the given information.