Directions: Read the following passage carefully and answer the question given…

Concept

In motion problems with a fixed speed ratio, first convert the ratio into actual speeds using the one known speed, then track each body's position over time as distance = speed x time. When a body reaches a turning point and reverses, its distance from the start is the outward distance minus the return distance; net displacement is not the same as total path length.

Application

1. Convert the ratio to real speeds. The ratio is P : Q : R = x : 1.25x : 0.5x, and Q's speed is 4 km/hr, so 1.25x = 4, giving x = 3.2. Hence P = 3.2 km/hr, Q = 4 km/hr, R = 1.6 km/hr.

2. Locate the meeting. Q starts at 9 am and meets P four hours later, i.e. at 1 pm. In those 4 hours Q covers 4 x 4 = 16 km, so the meeting point is 16 km from the start. (Check: P started at 8 am, so by 1 pm P has travelled 5 x 3.2 = 16 km too, confirming they meet at the same 16 km mark.)

3. Apply the reversal. At the meeting Q turns back. "Five hours" is measured from Q's 9 am start, i.e. up to 2 pm, which is 1 hour after the 1 pm meeting. In that 1 hour Q travels back 4 x 1 = 4 km.

4. Combine. Distance of Q from the start at 2 pm = 16 - 4 = 12 km.

Cross-check

Distinguish total path walked from straight-line distance to the start:

Reading the 20 km total path as the distance-from-start is the classic trap; the question asks for distance from the starting point, which is 12 km.