a park has 4 hiking trails. Trails A and B go from the lodge to the dock. Trail A is 1/2 mile long, and Trail B is 2/3 mile long. Trails C and D go from the dock to the park entrance. Trail C is 1/4 mile long and trail D is 1/3 mile long. Draw a picture of the possible trails. How long is each possible hike from the lodge to the dock and to the park entrance.
To draw a picture of the possible trails, you can use a simple diagram. Let's represent the lodge as 'L', the dock as 'D', and the park entrance as 'E'.
```
L ---------------------------> D --------------------------------------------> E
Trail A (1/2 mile) Trail C (1/4 mile)
L ---------------------------> D --------------------------------------------> E
Trail A (1/2 mile) Trail D (1/3 mile)
L ---------------------------> D --------------------------------------------> E
Trail B (2/3 mile) Trail C (1/4 mile)
L ---------------------------> D --------------------------------------------> E
Trail B (2/3 mile) Trail D (1/3 mile)
```
Now, to find the length of each possible hike from the lodge to the dock or to the park entrance, we can add up the distances mentioned for each trail.
Hike from the lodge to the dock:
- Trail A (1/2 mile) + Trail C (1/4 mile) = 3/4 mile
- Trail A (1/2 mile) + Trail D (1/3 mile) = 5/6 mile
- Trail B (2/3 mile) + Trail C (1/4 mile) = 7/12 mile
- Trail B (2/3 mile) + Trail D (1/3 mile) = 7/9 mile
Hike from the dock to the park entrance:
- Trail C (1/4 mile)
- Trail D (1/3 mile)
So, the lengths of each possible hike from the lodge to the dock are 3/4 mile, 5/6 mile, 7/12 mile, and 7/9 mile. The lengths of each hike from the dock to the park entrance can be seen from the diagram as 1/4 mile for Trail C and 1/3 mile for Trail D.