Dave and Sue leave the baseball stadium at the same time and in the same direction. After 2 hours, Sue is 102 miles ahead of Dave. Sue's speed is 3 more than 4 times Dave's speed. Find the speeds of Dave and Sue.

Question

whpalmer4 · Answer

Write equations to show the relationships.  
First, Sue's speed relative to Dave's speed:$$V_{Sue} = V_{Dave}*4 + 3$$
Next, distance traveled by each in 2 hours is given by $x = V*t$, so
$$x_{Sue} = V_{Sue}*2$$$$x_{Dave} = V_{Dave}*2$$
We know that in those 2 hours, Sue travels 102 miles more than Dave does, so$$x_{Sue}-x_{Dave} = 102$$
If you substitute the middle set of equations into the final equation, and then the first equation into the resulting equation, you'll get an equation for $V_{Dave}$.  Solve that, then use the first equation to find $V_{Sue}$.  Finally, plug your answers in and make sure that they give you a correct answer!