A cheetauh running 90 feet per second is 100 feet behind Gazelle running 70 feet per second. How long will it take the cheetah to catch up to the gazelle?Write and solve a linear eguation. and how do you do multi step equations 24-6r=6(4-r) please explain
The relative velocity is what is important. Cheeta is going 20f/s faster than gazelle, and has to make up a distance of 100 ft.
distance=relativevelcotiy*time
On the multistep...you need to post a specific problem.
To find the time it will take for the cheetah to catch up to the gazelle, we can set up a linear equation using the relative velocity and the distance between them.
Let t represent the time it will take for the cheetah to catch up to the gazelle.
Relative velocity of the cheetah = 90 ft/s - 70 ft/s = 20 ft/s
The distance the cheetah needs to make up is 100 ft.
So the equation becomes:
20 ft/s * t = 100 ft
To solve for t, we divide both sides of the equation by 20 ft/s:
t = 100 ft / 20 ft/s
t = 5 seconds
Therefore, it will take the cheetah 5 seconds to catch up to the gazelle.
Now, let's explain how to solve the multi-step equation: 24 - 6r = 6(4 - r)
To solve this equation, we can follow these steps:
Step 1: Distribute the 6 on the right side of the equation:
24 - 6r = 24 - 6r
Step 2: Simplify the equation by combining like terms:
24 - 6r = 24 - 6r
Step 3: Move the variable terms to one side and the constant terms to the other side. In this case, let's move the -6r term to the left side:
-6r + 6r = 24 - 24
The -6r and +6r terms cancel each other out, and we are left with:
0 = 0
Step 4: Since 0 = 0 is always true, this equation has infinite solutions. This means that any value of r will satisfy the equation.
In conclusion, the equation 24 - 6r = 6(4 - r) has infinite solutions.