To solve this problem, let’s define the following variables and equations:

• Let $d$ be the distance (in miles) from the starting point to the summit.
• Let $t$ be the time (in hours) it takes Vee to descend the distance.

Step 1: Write Equations for Time

Vee walks:

• Up the Grand Canyon at 1.5 mph, so the time taken for the uphill trip is $\frac{d}{1.5}$.
• Down the Grand Canyon at 2 mph, so the time taken for the downhill trip is $\frac{d}{2}$.

Step 2: Relate the Times

We know that it takes 5 hours longer for Vee to go up than to come down. Thus, we can write:

$\frac{d}{1.5} = \frac{d}{2} + 5$

Step 3: Solve for $d$

To eliminate the fractions, find the least common multiple of 1.5 and 2, which is 6. Multiply both sides of the equation by 6:

$6 \cdot \frac{d}{1.5} = 6 \cdot \left(\frac{d}{2} + 5\right)$

This simplifies to:

$4d = 3d + 30$

Step 4: Simplify and Solve

Subtract $3d$ from both sides:

$d = 30$

So, the distance from the starting point to the summit is 30 miles.

Final Answer:

Vee was 30 miles away from the starting point at the summit.

Would you like more details or have any questions?

Here are 5 related questions to deepen understanding:

1. How would the answer change if Vee walked downhill at 1 mph instead?
2. What would be the new distance if it took Vee only 3 hours longer to go uphill?
3. How can you set up a similar problem if Vee takes 4 hours longer uphill, but the rates are reversed?
4. How does the problem change if Vee's uphill speed was 2.5 mph and downhill speed was 3 mph?
5. How would you graph the relationship between time and distance for Vee’s journey?

Tip: When dealing with problems that involve different speeds and time differences, set up equations based on distance-time relationships and then solve systematically.