A distance–time graph shows two hikers, P and Q, who start walking from the same point at the same time. Hiker P's line is a straight line from (0 s, 0 m) to (40 s, 240 m). Hiker Q's line is a straight line from (0 s, 0 m) to (40 s, 160 m). Which hiker is walking faster, and wha…

Answer: A. Step 1: Calculate each hiker's speed Speed is the gradient of a distance–time graph, v = s/t. Both hikers walk for the same time, 40 s, so their speeds can be compared directly from the distance each one covers. For hiker P: vP = 240 m/40…

IGCSE Physics 0625: Comparing Speeds from Two Lines on a Distance-Time Graph

Step 1: Calculate each hiker’s speed

Speed is the gradient of a distance–time graph, $v = \dfrac{s}{t}$ . Both hikers walk for the same time, $40\text{ s}$ , so their speeds can be compared directly from the distance each one covers.

For hiker P: $v_P = \frac{240\text{ m}}{40\text{ s}} = 6.0\text{ m/s}$

For hiker Q: $v_Q = \frac{160\text{ m}}{40\text{ s}} = 4.0\text{ m/s}$

Step 2: Compare the two speeds

Since $6.0\text{ m/s} > 4.0\text{ m/s}$ , hiker P is walking faster. P’s line is also the steeper of the two lines on the graph, which is consistent with a distance-time graph: a steeper gradient always means a greater speed.

The difference between their speeds is: $6.0\text{ m/s} - 4.0\text{ m/s} = 2.0\text{ m/s}$

Why the other options are wrong

Option	What it claims	Why it’s wrong
B	Q faster, difference $2.0\text{ m/s}$	Gets the difference right but names the slower hiker (Q) as faster
C	P faster, difference $6.0\text{ m/s}$	Uses P’s own speed as the “difference” instead of subtracting Q’s speed from it
D	P faster, difference $10\text{ m/s}$	Adds the two speeds ( $6.0 + 4.0$ ) instead of subtracting them

Final answers

Hiker P is faster, and the difference in their speeds is $2.0\text{ m/s}$ , option A