Question

3 how far from home did the student travel after 30 minutes? a 5 km b 7.5 km c 10 km

Explanation:

Step1: Analyze the graph

The x - axis represents time (in minutes) and the y - axis represents distance from home (in km). We need to find the distance at \(t = 30\) minutes. Looking at the graph, the point \(E\) is at \(t=30\) minutes. The horizontal line from \(D\) to \(E\) shows that the distance remains constant from \(t = 20\) to \(t=30\) minutes. From the graph, the \(y\) - coordinate (distance) at \(t = 30\) minutes (point \(E\)) is the same as at \(t = 20\) minutes (point \(D\)), which is \(7.5\) km? Wait, no, looking at the grid, each square on the \(y\) - axis: from \(0\) to \(5\) is one interval, then \(5\) to \(10\) is another. Wait, point \(D\) is at \(y = 7.5\)? No, wait, maybe I misread. Wait, the graph: at \(t = 20\) minutes, the distance is \(7.5\) km? Wait, no, let's check the grid again. Wait, the vertical axis: the first grid line above \(0\) is \(5\) km? Wait, no, the graph has points: \(B\) is at \(t = 5\) minutes, \(y = 5\) km. Then \(C\) is at \(t = 15\) minutes, \(y = 0\) km. Then \(D\) is at \(t = 20\) minutes, \(y = 7.5\) km? No, wait, maybe each small square is \(2.5\) km? Wait, no, the options are \(5\), \(7.5\), \(10\). Wait, looking at the graph, from \(t = 20\) to \(t = 30\), the distance is constant. At \(t = 20\), the distance is \(7.5\) km? No, wait, maybe the correct way: the graph's \(y\) - axis: the point \(D\) is at \(y=7.5\)? Wait, no, the option \(B\) is \(7.5\) km. Wait, let's re - examine. The graph: at \(t = 30\) minutes, the distance is the same as at \(t = 20\) minutes. From the graph, the \(y\) - coordinate at \(t = 30\) (point \(E\)) is \(7.5\) km? Wait, no, maybe I made a mistake. Wait, the options: \(A\) is \(5\) km, \(B\) is \(7.5\) km, \(C\) is \(10\) km. Wait, looking at the graph, the horizontal line from \(D\) to \(E\): the \(y\) - value of \(D\) and \(E\) is \(7.5\) km? Wait, no, maybe the grid is such that each square is \(2.5\) km. So from \(0\) to \(5\) is two squares (each \(2.5\) km), then \(5\) to \(10\) is two squares. Wait, point \(D\) is at \(y = 7.5\) km (three squares of \(2.5\) km each: \(2.5\times3 = 7.5\)). So at \(t = 30\) minutes, the distance is \(7.5\) km.

Step2: Confirm the answer from the options

Among the options, option \(B\) is \(7.5\) km.

Answer:

B. 7.5 km