Final answer:
Taylor and Dakota meet after 3 hours, with Dakota traveling 4 mph faster. Setting the equation 3x + 3(x + 4) = 48 and solving for x gives Taylor's speed as 6 mph, Dakota's as 10 mph. This does not match the options provided, indicating a possible error in the question or options.
Step-by-step explanation:
The student's question involves determining the speeds at which Taylor and Dakota are traveling if they start 48 miles apart and meet after 3 hours, with Dakota traveling 4 mph faster than Taylor. We can solve this problem by setting up equations based on the relationship between distance, rate (speed), and time.
Let Taylor's speed be x mph. Since Dakota's speed is 4 mph faster, Dakota's speed is x + 4 mph. They meet after 3 hours, so combining their distances traveled gives us the total distance:
Taylor's distance + Dakota's distance = Total distance
3x + 3(x + 4) = 48
Expanding this we get:
3x + 3x + 12 = 48
Combining like terms, we have:
6x + 12 = 48
Subtracting 12 from both sides gives us:
6x = 36
Dividing by 6, we find:
x = 6
Therefore, Taylor's speed is 6 mph, and Dakota's speed is 6 + 4 = 10 mph. However, none of the options provided match our calculation. It seems there may be a mistake in either the question or the options provided. The correct speeds should be recalculated or clarified for an accurate answer.