10. Harriet took 48 minutes to ride her bike the distance from her house to the town library. If she rode at a constant rate, what fraction of the total distance did she ride in the first 12 minutes?
Answer: A
Harriet rode 1/4 of the total distance in the first 12 minutes.
Since Harriet took 48 minutes to cover the entire distance to the library, in the first 12 minutes, she would have covered a fraction of the total distance. Specifically, 12 minutes is one-fourth of 48 minutes, indicating she rode 1/4 of the total distance.
A) 1/4
This option is correct because 12 minutes represents one-fourth of the total 48 minutes it took Harriet to reach the library. Therefore, the distance covered in the first 12 minutes is indeed 1/4 of the total distance.
B) 1/3
Option B is incorrect because 1/3 of the total distance would imply that in 16 minutes, Harriet would have reached that fraction of the total distance. Since she only traveled for 12 minutes, this does not accurately reflect the time taken.
C) 1/2
This option is also incorrect. If Harriet had ridden half of the total distance, she would have taken 24 minutes (half of 48 minutes) to cover that distance. Since she only rode for 12 minutes, she did not cover half of the distance.
D) 3/4
Option D is incorrect as well. Riding 3/4 of the distance would have required Harriet to ride for 36 minutes (3/4 of 48 minutes). Since she only rode for 12 minutes, this option does not reflect the actual distance traveled.
Conclusion
In conclusion, the correct answer, 1/4, accurately represents the fraction of the total distance Harriet rode in the first 12 minutes. All other options fail to correspond to the time she spent riding relative to the total time, making them incorrect. Thus, understanding the relationship between time and distance is essential to solving this problem accurately.