You are going for a bike ride. You ride down a straight road at a speed of 9.0 mi/hr. Just as you pass the point which is 3.6 miles from your starting point, you develop a flat tire. You get off your bike and walk it to a bike shop 0.5 miles further down the road. The walk to the bike shop takes 12 minutes. What was the average velocity for the entire trip?

d = 3.6 + 0.5 = 4.1 miles.

T1 = 3.6/9 + 12/60 = 0.6 hr. To travel
4.1 miles from starting point.
V1 = d/T1 = 4.1/0.6 = 6.83 mi/h.

V2=9.0 mi/h. when returning to starting
point.

V = (V1+V2)/2 = (6.83+9.0)/2 = 7.92 mi/h
= Average velocity for entire trip.

To find the average velocity for the entire trip, we need to calculate the total displacement and the total time taken.

1. First, let's calculate the total displacement:
- You rode 3.6 miles down the road before getting a flat tire.
- Then, you walked 0.5 miles to the bike shop.
- Therefore, the total displacement is 3.6 + 0.5 = 4.1 miles.

2. Next, let's calculate the total time taken:
- The time taken for the bike ride alone can be found by dividing the distance by the speed:
Time = Distance / Speed = 3.6 miles / 9.0 mi/hr = 0.4 hours.
- The time taken for the walk to the bike shop is given as 12 minutes. We need to convert it to hours by dividing by 60:
Time = 12 minutes / 60 = 0.2 hours.
- Therefore, the total time taken for the entire trip is 0.4 hours + 0.2 hours = 0.6 hours.

3. Finally, let's find the average velocity:
- Average velocity is defined as displacement divided by time:
Average Velocity = Total Displacement / Total Time = 4.1 miles / 0.6 hours.
- Simplifying, we get: Average Velocity = 6.83 mi/hr.

Therefore, the average velocity for the entire trip is 6.83 mi/hr.

To find the average velocity for the entire trip, we need to calculate the total displacement and the total time taken.

Let's break down the trip into two parts:

1. Biking from the starting point to the point where the flat tire occurred.
2. Walking from the point of the flat tire to the bike shop.

For the first part:
Distance covered while biking = 3.6 miles.
Time taken for biking = Distance / Speed = 3.6 miles / 9.0 mi/hr = 0.4 hours.

For the second part:
Distance covered while walking = 0.5 miles.
Time taken for walking = 12 minutes = 12/60 hours = 0.2 hours.

Now, let's calculate the total displacement and total time for the entire trip:

Total displacement = Final position - Initial position = (3.6 miles + 0.5 miles) = 4.1 miles.
Total time = Time for biking + Time for walking = 0.4 hours + 0.2 hours = 0.6 hours.

Finally, we can calculate the average velocity for the entire trip:

Average velocity = Total displacement / Total time = 4.1 miles / 0.6 hours ≈ 6.83 mi/hr.

Therefore, the average velocity for the entire trip is approximately 6.83 mi/hr.