In which of the following graphs below are both runners moving at the same speed?

In a linear equation, like the ones in the graphs, the slope is equivalent to the rate of change. And we know that speed is defined as the rate of the position, thus the slope of these lines is exactly equal to the speed.

From this, we will see that the correct option is D.

Knowing this, two runners will have exactly the same speed if and only if both slopes (one for each runner) are exactly equal. This means that we will see two parallel lines.

This makes a lot of sense, because if they run at the same speed, then they will never meet (like two parallel lines), instead if they run at different speeds and the one that is behind runs faster, at some given point the one that goes last will reach the other, and in this point we would see that the lines intersect in the graph (like in options A, B, and C).

So from this we already can see the correct option, it is the graph with the two parallel lines, the graph D.

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Explanation:

In this case, we need to identify the graph in which both the runners are moving at the same speed. All the graphs shows distance time graphs.

The attached graph shows that the both runners are moving with same speed. Both the objects have same slope.

The slope of the graph is given by :

Also, both lines are parallel to each other and two parallel lines have same slope. So, in figure (d), both runners are moving at the same speed.

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