Places A and B are 20 km apart on the highway. A car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in one hour. If they travelled towards each other, they met in 12 minutes. What are the speeds (in km/h) of two cars?

Question

Accepted Answer

Let the speeds of the two cars be x km/h and y km/h, with x > y.

Given:
- Distance between A and B = 20 km
- When moving in the same direction, they meet in 1 hour.
- When moving towards each other, they meet in 12 minutes (which is 1/5 hour).

Case 1: Same direction
Relative speed = x - y
Time to meet = 1 hour
Distance covered in 1 hour = 20 km
So, x - y = 20 km/h ...(1)

Case 2: Opposite direction
Relative speed = x + y
Time to meet = 12 minutes = 1/5 hour
Distance covered in 1/5 hour = 20 km
So, (x + y) × (1/5) = 20
=> x + y = 100 km/h ...(2)

Now, solve the two equations:
From (1): x - y = 20
From (2): x + y = 100

Add both equations:
2x = 120 => x = 60 km/h

Subtract (1) from (2):
2y = 80 => y = 40 km/h

Therefore, the speeds of the two cars are 60 km/h and 40 km/h.

Final Answer: Option 1 (60, 40)

Answer

Answer

Answer