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.
Whole numbers include 0, 1, 2, 3, 4, 5, and so forth.
There are 56 pairs of whole numbers that add up to 110, such as:
0 + 110 = 110
1 + 109 = 110
2 + 108 = 110
.
.
.
.
.
55 + 55 = 110
Thus, the total count of pairs is 56.
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