Alice and Briana each participate in a 5 kilometer race. Alice's distance covered, in kilometers, after t minutes can be modeled

Answer:

a) Alice moves first, b) Briana finishes the race ahead, c)

Step-by-step explanation:

a) Alice gets underway first, since the binomial under the square root becomes zero when , while Alice starts at .

b) The moment each runner crosses the finish line is:

Alice

Briana

Briana reaches the finish before Alice.

c) Alice and Briana are at the same point when . From here:

The roots of the polynomial are:

and

Only the second root is relevant, as they must be parallel at some point prior to finishing the race.

Answer:

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice's formula is applicable for any t > 0 minutes, while Briana’s is only applicable when

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They complete the race when their total distance equals 5 kilometers. For Alice:

t/4 = 5

t = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 25

2t = 26

t = 13 minutes

c. They reach the same point when they have traveled the same distance, expressed as:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using the quadratic formula:

Only the second solution fits this scenario because the race concluded before they took 31.49 minutes.