a fishing boat left port 26 and traveled toward st.vincent.Two hours later a cruise ship left traveling at 30km/h in an effort to catch up to the finishing boat.After traveling for four hours the cruise ship finally caught up.What was the fishing boats speed

We can solve this problem by setting up an equation based on the information given.

Let's define:
- \( v \) as the speed of the fishing boat in km/h.
- The cruise ship's speed is \( 30 \, \text{km/h} \).
- The fishing boat had a 2-hour head start, so it traveled for 6 hours when the cruise ship caught up (2 hours before the cruise ship started, plus 4 hours while the cruise ship was traveling).

### Step-by-Step Solution:

1. **Distance traveled by the fishing boat:**
   The fishing boat traveled for 6 hours at a speed of \( v \, \text{km/h} \). Therefore, the distance it covered is:
   \[
   \text{Distance by fishing boat} = 6v \, \text{km}.
   \]

2. **Distance traveled by the cruise ship:**
   The cruise ship traveled for 4 hours at a speed of \( 30 \, \text{km/h} \). Therefore, the distance it covered is:
   \[
   \text{Distance by cruise ship} = 30 \times 4 = 120 \, \text{km}.
   \]

3. **Setting up the equation:**
   Since both the fishing boat and the cruise ship covered the same distance when the cruise ship caught up, we can equate their distances:
   \[
   6v = 120.
   \]

4. **Solving for \( v \):**
   \[
   v = \frac{120}{6} = 20 \, \text{km/h}.
   \]

Thus, the speed of the fishing boat is **20 km/h**.

Would you like more details on this solution? Here are 5 related questions:

1. If the fishing boat traveled for 10 hours, how far would it go?
2. How much longer would it take for the cruise ship to catch up if its speed was 25 km/h instead?
3. What would the equation look like if the fishing boat had traveled for 3 hours before the cruise ship started?
4. How far apart were the two boats when the cruise ship started?
5. If the fishing boat's speed was reduced by 5 km/h, how long would it take for the cruise ship to catch up?

**Tip:** When setting up distance equations, always remember to multiply speed by time to find the distance.

A fishing boat left port 26 and traveled toward St. Vincent. Two hours later, a cruise ship left traveling at 30km/h in an effort to catch up to the fishing boat. After traveling for four hours, the cruise ship finally caught up. What was the fishing boat's speed?

Learn how to calculate the speed of a fishing boat using distance, speed, and time relationships. This step-by-step solution involves setting up an equation and solving for the unknown speed. Suitable for students in Grades 6-8, this problem explores basic algebra and distance-speed-time concepts.

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