Question

Two places A and B are 120 km apart on a highway. A car starts from A and another starts from B at the same time. If they go in the same direction they meet in 3 hours. If they go in opposite direction, they meet in one hour. Find the speeds of car A and car B.

Answer 1

Given:

• Two places A and B are 120 km apart on a highway.
• Two cars start from A and B at the same time.
• If both cars move in the same direction, they meet after 3 hours.
• If both cars move in opposite directions, they meet after 1 hour.
• Find the speeds of car A (x km/h) and car B (y km/h).

Step-wise calculation:

1. When the cars move in the same direction, the relative speed is the difference of their speeds, i.e. |x – y| km/h.

They meet after 3 hours, so:

Distance = Relative speed × Time

120 = |x – y| × 3

⇒ `|x - y| = 120/3` 

⇒ |x – y| = 40   ...(Equation 1)

2. When the cars move in opposite directions, the relative speed is the sum of their speeds, i.e. (x + y) km/h.

They meet after 1 hour, so:

Distance = Relative speed × Time

120 = (x + y) × 1

⇒ x + y = 120   ...(Equation 2)

3. From Equation 1: x – y = 40   ...(Assuming x > y)

From Equation 2: x + y = 120

4. Add the two equations to eliminate y:

(x – y) + (x + y) = 40 + 120

2x = 160

⇒ x = 80 km/h

5. Substitute x = 80 into Equation 2:

80 + y = 120

⇒ y = 40 km/h

The speed of car A is 80 km/h and the speed of car B is 40 km/h.