To solve this problem, we can use the Pythagorean theorem. The two boats are traveling at right angles to each other (north and west), forming a right triangle where the boats' distances traveled are the legs of the triangle.

Given:

• Speed of boat 1 (northward) = $35 \, \text{km/h}$
• Speed of boat 2 (westward) = $15 \, \text{km/h}$
• Time traveled = $1 \, \text{hour}$

After 1 hour:

• Distance traveled by boat 1 (northward) = $35 \, \text{km}$
• Distance traveled by boat 2 (westward) = $15 \, \text{km}$

Now, we can apply the Pythagorean theorem:

$d^2 = (35)^2 + (15)^2$ $d^2 = 1225 + 225$ $d^2 = 1450$ $d = \sqrt{1450}$ $d \approx 38.07 \, \text{km}$

Answer:

The boats are approximately 38.07 kilometers apart after 1 hour.

Would you like further explanation on the Pythagorean theorem, or is there anything else you'd like to ask?

Here are a few related questions you might find interesting:

1. How would the distance change if the boats were traveling at the same speed?
2. What happens if the boats are traveling in the same direction?
3. How do you calculate the distance between two objects moving towards each other?
4. Can this problem be solved using vector addition instead of the Pythagorean theorem?
5. How would the boats' distance change if the time was 2 hours instead of 1 hour?

Tip: For right-angled triangle problems involving distance, speed, and time, always remember the Pythagorean theorem or consider using trigonometric relationships if angles are involved.