She ran 15 miles at a quicker speed based on the information supplied. See explanation below. This is a distance time problem.
<h3>What is the justification for the above result?</h3>
The distances between the two "half" of the race are our unknowns here. We must assign them to variables - Alicia ran x miles in the first half of the race and y miles in the second.
Since the race is 21 miles in total, x and y together must add up to 21.
Hence,
x + y = 21
The speeds at which she raced and the total time involved are then given; we can link this to the distances using the speed and distance equation
d = st, or t = d/s.
Because she completed in two hours, the hours spent running the first and second parts must sum up to two hours, or:
x/8 + y/12 = 2
Two equations are sufficient to solve for two unknowns. We can approach this by multiplying the second equation by the LCM, 24
3x + 2y = 48
And rearrange the first to get y = 21 - x, which we can plug into the above. This gives us:
3x + 2(21 - x) = 48
3x + 42 - 2x = 48
x = 6
Use y = 21 - x again:
y = 21 - (6) = 15.
Recall that the question asks how long she ran at the faster speed - this would be the second half of the race, which we've labeled y, so 15 miles. But first, let's make sure our solution works.
Obviously, 15 + 6 = 21, thus the overall distance is correct.
In terms of time, 6 miles at 8 mph takes
6/8 =.75 hours = 45 minutes, whereas
15 miles at 12 mph takes 15/12 = 1.25 hours = 75 minutes.
As stated in the question, the total time to complete would be.
75 + 1.25 = 2 hours.
As a result, this solution is correct, as Alicia ran 15 miles at a quicker rate.
Learn more about distance time:
brainly.com/question/4931057
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