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To solve the problem, we need to apply the concept of proportionality. Let's break down the information:

- A crew of 45 men has provisions for 60 days.
- They want to increase the crew size by 15 men, making the total 60 men.

We need to find out how many days the provisions will last with the new crew size.

### Step 1: Calculate the total amount of provisions in "man-days."
Provisions for 45 men for 60 days mean that the total provisions can be measured as:
\[ \text{Total Provisions} = 45 \times 60 = 2700 \text{ man-days} \]

### Step 2: Determine the new duration.
With the crew increased to 60 men, we need to find out how many days (\(x\)) the provisions will last:
\[ 60 \times x = 2700 \]

Solve for \(x\):
\[ x = \frac{2700}{60} = 45 \text{ days} \]

So, the provisions will last for 45 days if the crew is increased to 60 men.

### Final Answer:
The duration of the trip should be adjusted to 45 days. However, this answer doesn't match any of the provided options. Upon reviewing the answer choices, it seems the correct interpretation is needed for the rounding or approximation, or we might check for any small changes in assumptions.

This indicates that the expected duration would have been simplified or approximated, potentially assuming any rounding or adjustments expected in practice. But the mathematically exact answer is 45 days.

Would you like further explanation or details? Here are some related questions:

1. How do you determine the total amount of provisions in a "man-days" unit?
2. What is the relationship between the number of men and the duration of provisions?
3. How would the solution change if the crew size was increased by a different number?
4. What is the general formula for problems involving proportions in provisions?
5. Can the trip be extended or reduced in time based on changing other variables like rationing?
6. How does the answer change if the provisions were only for 30 days originally?
7. What would happen if instead of increasing the crew, they decreased it?
8. How can this type of problem be applied to other resource management scenarios?

**Tip:** When working with proportion problems, always ensure your units are consistent throughout the calculations to avoid mistakes.

Learn how to calculate the duration of provisions when increasing crew size based on proportional relationships. Solve a practical problem involving crew size and provision duration using basic arithmetic and proportionality concepts.

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