Question

Tatiana walked part of the 10-mile distance at 2 miles per hour and rode her bicycle the rest of the way at 12 miles per hour. If the whole trip took 1 hour, how much time did she spend walking?

a. 1/3 hour
b. 1/4 hour
c. 1/5 hour
d. 1/6 hour

Answer 1

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