Final answer:
The correct answer is option b. 1/4 hour. By setting up an equation using time, distance, and speed for both walking and bicycling parts of Tatiana's trip, we can solve for the time spent walking.
Step-by-step explanation:
The correct answer is option b. 1/4 hour. To determine how much time Tatiana spent walking, we need to set up an equation based on the total time and the distances covered at different speeds. Let's define the time spent walking as t hours and the time spent riding her bicycle as 1 - t hours (since the whole trip takes 1 hour).
- Walking speed = 2 miles/hour
- Bicycling speed = 12 miles/hour
- Total distance = 10 miles
- Total time = 1 hour
Distance walked = walking speed × time walked = 2 miles/hour × t hours
Distance bicycled = bicycling speed × time bicycled = 12 miles/hour × (1 - t) hours
Since the total distance is 10 miles, these two distances must add up to 10:
2t + 12(1 - t) = 10
Solving for t we get:
10 = 2t + 12 - 12t
10 = 12 - 10t
10t = 2
t = 1/5