A car travels at an average speed of 60 km/h for 2 hours. 
It then travels at an average speed of x km/h for 3 hours.
 The car travels at an average speed of 64.2 km/h for the whole journey.
 Calculate the value of x


To solve for the value of \( x \), we can use the concept of average speed, which is defined as the total distance traveled divided by the total time taken.

### Step 1: Calculate the total distance traveled
1. **Distance traveled in the first part of the journey:**
   \[
   \text{Distance}_1 = \text{Speed}_1 \times \text{Time}_1 = 60 \, \text{km/h} \times 2 \, \text{h} = 120 \, \text{km}
   \]

2. **Distance traveled in the second part of the journey:**
   \[
   \text{Distance}_2 = \text{Speed}_2 \times \text{Time}_2 = x \, \text{km/h} \times 3 \, \text{h} = 3x \, \text{km}
   \]

3. **Total distance:**
   \[
   \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 = 120 \, \text{km} + 3x \, \text{km}
   \]

### Step 2: Calculate the total time taken
The total time is:
\[
\text{Total Time} = 2 \, \text{h} + 3 \, \text{h} = 5 \, \text{h}
\]

### Step 3: Use the average speed formula
The average speed for the whole journey is given by:
\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
\]
Substituting the values we have:
\[
64.2 = \frac{120 + 3x}{5}
\]

### Step 4: Solve for \( x \)
Multiply both sides of the equation by 5:
\[
321 = 120 + 3x
\]
Subtract 120 from both sides:
\[
201 = 3x
\]
Finally, divide by 3:
\[
x = \frac{201}{3} = 67 \, \text{km/h}
\]

So, the value of \( x \) is **67 km/h**.

Would you like a more detailed explanation or have any questions?

Here are some related problems you might find interesting:
1. What would be the average speed if the second part of the journey was 4 hours instead of 3?
2. How would the value of \( x \) change if the car traveled 70 km/h in the first part?
3. If the total time was reduced to 4 hours, what would be the new average speed?
4. How would the value of \( x \) change if the total average speed was 66 km/h?
5. What is the total distance traveled if \( x \) is 75 km/h?

**Tip:** Always double-check your units when solving speed, distance, and time problems to ensure accuracy.

Learn how to calculate the average speed of a car that travels at two different speeds for specified durations. This problem involves calculating distances, using the average speed formula, and solving for unknown speeds. Suitable for Grades 7-9 students.

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