Question

Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different speeds, they will meet in 2 hours. Had they walked in the same direction with same speeds as before, they would have met in 8 hours. Find their walking speeds.

Answer 1

Given: Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other they meet in 2 hours; if they walk in the same direction they meet in 8 hours.

Step-wise calculation:

1. Let the speeds be x km/h and y km/h, with x > y.

2. Toward each other: Relative speed = x + y.

Meeting time = 2 h.

So `x + y = 16/2 = 8`.

3. Same direction: Relative speed = x – y.

Meeting time = 8 h.

So `x - y = 16/8 = 2`.

4. Solve the system:

x + y = 8

x – y = 2

Add: 2x = 10

⇒ x = 5 km/h.

Then y = 8 – x

= 8 – 5

= 3 km/h

5. Check: Towards each other:

`16/(5 + 3) = 16/8`

= 2 h

Same direction:

`16/(5 - 3) = 16/2`

= 8 h

The two walking speeds are 5 km/h and 3 km/h.