Question

I traveled

your
5. Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second
ahead of the starting line. Let y represent the distance from the starting line and x re
the time elapsed, in seconds. Write an equation to model the distance Aidan t
an equation to model the distance Ella traveled. On the set of axes below, graph y
equations.
near Systems
Feet
150
100
50
0
5
10
15
X
Linear
Seconds
Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.

Answer 1

Aiden will catch up to Ella in 7.5 seconds, covering 75 feet, while Ella covers her initial distance of 30 feet.

The distance Aiden covers (DA) is given by the product of his rate (RA) and time (t):

DA = RA * t

The distance Ella covers (DE) is given by the product of her rate (RE) and time (t):

DE = RE * t

Ella starts 30 feet ahead, so her initial distance (DE0) is:

DE0 = 30

At the time Aiden catches up to Ella, their distances will be equal:

DA = DE + DE0

Substituting in the expressions for DA, DE, and DE0:

RA * t = RE * t + DE0

Now, plug in the given rates:

10t = 6t + 30

Subtract 6t from both sides:

4t = 30

Divide both sides by 4:

t = 30/4

Simplify:

t = 7.5

So, it will take 7.5 seconds for Aiden to catch up to Ella. You can find the distance they each cover by plugging this time back into either DA or DE:

DA = 10 * 7.5 = 75

Thus, Aiden will have covered 75 feet, and Ella will have covered 30 feet (her initial distance).

Complete question:

Aiden and his sister ella are having a race. Aiden runs at a rate of 10 feet per second. ella runs at a rate of 6 feet per socond. since ella is younger, aiden is letting her begin 30 feet ahead of the starting line.