3 A man travels 360 m along a straight road. He walks for the first 120 m at \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), runs the next 180 m at \(4.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and then walks the final 60 m at \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The man's displacement from his starting point after \(t\) seconds is \(x\) metres.

1. Sketch the \(( t , x )\) graph for the journey, showing the values of \(t\) for which \(x = 120,300\) and 360 . A woman jogs the same 360 m route at constant speed, starting at the same instant as the man and finishing at the same instant as the man.
2. Draw a dotted line on your ( \(t , x\) ) graph to represent the woman's journey.
3. Calculate the value of \(t\) at which the man overtakes the woman.