A6. To travel the 140 kilometres between Glasgow and Dundee, John travels half an hour by bus and two hours by train. The train travels $20 \mathrm{~km} / \mathrm{h}$ faster than the bus. The bus and the train both travel at constant speeds. What is the speed of the bus?
Solution
$40 \mathrm{~km} / \mathrm{h}$

Let the speed of the bus be $v \mathrm{~km} / \mathrm{h}$. Then the speed of the train is $(v+20) \mathrm{km} / \mathrm{h}$. Therefore $\frac{1}{2} \times v+2 \times(v+20)=140$. So $\frac{5 v}{2}+40=140$. Hence $v=\frac{2 \times 100}{5}=40$.