Question 58959
If Smith's speed is x then Jones speed is x+5.
The time taken by Smith is 45/x and the time taken by Jones is 70/(x+5). Jones time is 0.5 hour long than Smith so
{{{45/x+0.5=70/(x+5)}}} 
Multiply through by x to get
{{{45+0.5x=70x/(x+5)}}} 
Multiply through by (x+5)
{{{45(x+5)+0.5x(x+5)=70x}}} 
{{{45x+225+0.5x^2+2.5x=70x}}} 
{{{0.5x^2+47.5x+225=70x}}} 
{{{0.5x^2-22.5x+225=0}}} 
{{{x^2-45x+450=0}}}
{{{(x-15)(x-30)=0}}}
So Smith's speed is either 15 miles per hour or 30 miles per hour. Jones speed will therefore be 20 miles per hour or 35 miles per hour. 
At the slower speed Smith takes 3.0 hours and Jones takes 3.5 hours while at the faster speed Smith takes 1.5 hours and Jones takes 2.0 hours.