Arthur and Betty start walking toward each other when they are 100 m apart. Arthur has a
speed of 3.0 m/s and Betty has a speed of 2.0 m/s. Their dog, Spot, starts by Arthur's side at
the same time and runs back and forth between them at 5.0 m/s. By the time Arthur and
Betty meet, what distance has Spot run?

Question

Arthur and Betty start walking toward each other when they are 100 m apart. Arthur has a
speed of 3.0 m/s and Betty has a speed of 2.0 m/s. Their dog, Spot, starts by Arthur's side at
the same time and runs back and forth between them at 5.0 m/s. By the time Arthur and
Betty meet, what distance has Spot run?

anonymous · Answer

|dw:1401635611453:dw|
Suppose, Arthur and Betty meet at the point C.
We know that:
$\Large S_A=v_At$
$\Large S_B=-v_Bt$
When they meet, $\Large S_A+S_B=L \Leftrightarrow v_At - v_Bt=L$ 
                         $\Large 3t-2t=100 \Rightarrow t=100$ $\large s$
So, Spot run distance: $\Large S_S=v_St=5\times 100=500$ $\large m$