Places A and B are 80 km apart on a highway. A car starts from A and another from B at the same time. If they move towards each other, they meet in 1 hr 20 min. Find the speed of the cars.

To solve this problem, let's first break it down step by step.

### Step 1: Convert the time
The time taken for the two cars to meet is given as 1 hour and 20 minutes. Convert 20 minutes into hours:
\[
\text{20 minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours} \approx 0.333 \text{ hours}
\]
So, the total time is:
\[
1 \text{ hour } 20 \text{ minutes} = 1 + \frac{1}{3} = \frac{4}{3} \text{ hours}
\]

### Step 2: Set up the relationship between distance, speed, and time
Let the speed of the car starting from A be \(v_A\) km/h and the speed of the car starting from B be \(v_B\) km/h.

Since the cars are moving towards each other, their relative speed is the sum of their speeds:
\[
v_A + v_B
\]
The distance between A and B is 80 km, and they meet in \(\frac{4}{3}\) hours. According to the relationship:
\[
\text{Distance} = \text{Relative Speed} \times \text{Time}
\]
We can write:
\[
80 = (v_A + v_B) \times \frac{4}{3}
\]

### Step 3: Solve for the relative speed
To find the relative speed, rearrange the equation:
\[
v_A + v_B = \frac{80 \times 3}{4} = 60 \text{ km/h}
\]
So, the combined speed of the two cars is 60 km/h.

### Step 4: Interpret the result
The sum of the speeds of both cars is 60 km/h. If additional information about the speed of one car were provided, you could determine the exact speeds of each car. However, with the given data, the sum of the speeds is all we can determine.

### Summary
The combined speed of the two cars is **60 km/h**.

Do you need further details or have any questions? Here are five related questions:

1. If one car was moving 10 km/h faster than the other, what would be their individual speeds?
2. How would the solution change if the distance was 100 km instead of 80 km?
3. What would happen if the cars moved in the same direction instead of towards each other?
4. How would the time taken change if one car started 10 minutes later?
5. What is the impact of a speed limit on such a problem?

**Tip:** Always convert time units to the same format (hours, minutes) when calculating speed, distance, or time.

Learn how to calculate the combined speed of two cars moving towards each other, given that they meet after 1 hr 20 min over a distance of 80 km. This problem covers key algebraic concepts related to time, distance, and relative speed. Suitable for students in Grades 7-10.

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