Question

Two places P and Q are 120 km apart from each other on a highway. A car starts from P and another from Q at the same time. If they move in the same direction, they meet each other in 8 hours. If they move in opposite directions towards each other, they meet in 2 hours 40 minutes. What are the respective speeds of the cars in km/hour?

• A. 30, 15
• B. 25, 20
• C. 45, 25
• D. 45, 30

Hint:

When two objects move towards or away from each other, use the relative speed (difference for same direction, sum for opposite directions) and apply the time and distance formula to solve.

Answer 1

The Correct Option is A

Let the speeds of the cars be \( x \) km/h and \( y \) km/h. Case 1: Moving in the same direction. When the cars move in the same direction, the relative speed is \( |x - y| \) km/h, and they meet after 8 hours. Therefore: \[ |x - y| \times 8 = 120 \quad \Rightarrow \quad |x - y| = \frac{120}{8} = 15. \] Case 2: Moving in opposite directions. When the cars move in opposite directions, their relative speed is \( x + y \) km/h, and they meet after 2 hours 40 minutes, or \( \frac{8}{3} \) hours. Therefore: \[ (x + y) \times \frac{8}{3} = 120 \quad \Rightarrow \quad x + y = \frac{120 \times 3}{8} = 45. \] Now, solving the system of equations: \[ |x - y| = 15 \quad \text{and} \quad x + y = 45. \] Adding these two equations: \[ (x + y) + (x - y) = 45 + 15 \quad \Rightarrow \quad 2x = 60 \quad \Rightarrow \quad x = 30. \] Substituting \( x = 30 \) into \( x + y = 45 \): \[ 30 + y = 45 \quad \Rightarrow \quad y = 15. \] Thus, the speeds of the cars are 30 km/h and 15 km/h.