Given:
- Two trains start at the same time from two stations 80 km apart and go in opposite directions.
- They meet each other after 20 minutes.
- The first train starts 16 minutes late from the second train.
- They meet after 10 minutes.

To find: The speed of the first train.

Let's solve this problem step by step:

1. Determine the relative speed of the two trains when they meet after 20 minutes.

Since the trains are traveling in opposite directions, their relative speed will be the sum of their individual speeds. Let's assume the speeds of the first and second trains are v1 and v2, respectively.

So, the relative speed of the two trains is given by:
Relative speed = v1 + v2

2. Calculate the distance covered by the trains when they meet after 20 minutes.

Since the relative speed is the sum of the individual speeds, the distance covered by the two trains when they meet after 20 minutes is given by:
Distance = Relative speed × Time
Distance = (v1 + v2) × 20

3. Determine the time taken by the first train to meet the second train when it starts 16 minutes late.

Since the first train starts 16 minutes late, it will have traveled for 20 - 16 = 4 minutes when it meets the second train.

4. Calculate the distance covered by the first train in 4 minutes.

Using the speed-time-distance equation, we can calculate the distance covered by the first train in 4 minutes:
Distance = Speed × Time
Distance = v1 × 4

5. Calculate the distance covered by the second train in 4 minutes.

Since the two trains meet after 20 minutes, and the first train has traveled for 4 minutes, the second train will have traveled for 20 - 4 = 16 minutes.

Using the speed-time-distance equation, we can calculate the distance covered by the second train in 16 minutes:
Distance = Speed × Time
Distance = v2 × 16

6. Calculate the total distance covered by the two trains when they meet after 20 minutes.

The total distance covered by the two trains when they meet after 20 minutes is the sum of the distances covered by each train:
Total Distance = Distance covered by first train + Distance covered by second train
Total Distance = v1 × 4 + v2 × 16

7. Set up an equation using the total distance covered when they meet after 20 minutes.

We know that the total distance covered by the two trains when they meet after 20 minutes is equal to the distance between the two stations, which is 80 km:
Total Distance = 80 km

So, we can write the equation as:
v1 × 4 + v2 × 16 = 80

8. Determine the time taken by the first train to meet the second train when it starts 16 minutes late.

Since the first train starts 16 minutes late and they meet after 10 minutes, the first train will have traveled for 10 - 16 = -6 minutes, which is not possible. This means that the trains did not meet after 10 minutes when the first train started 16 minutes late.

9. Calculate the speed of the first train.

Using the equation from step 7:
v1 × 4 + v2 × 16 = 80

We can substitute the values:
v1