Let [tex]x[/tex] be the amount of time it takes to perform an arm routine and [tex]y[/tex] be the amount of time it takes to perform an abdominal routine. We see:
[tex]4x+y=70[/tex]
[tex]4x+2y=100[/tex]
Subtracting the second equation from the first gives [tex]y=30[/tex]. Substituting gives [tex]4x+30=70[/tex], so [tex]4x=40[/tex] and [tex]x=10[/tex].
Thus, an arm routine takes ten minutes and an abdominal routine takes thirty minutes.
