Respuesta :
recall your d = rt, distance = rate * time
now, bear in mind that, for the police to overtake the robbers, they must first meet, and then overtake them.... well, clearly the cops don't want to overtake them, they want to arrest them, so if they just pass by the robbers, not much there, but anyway.
if the robbers had travelled a "d" miles, when the cops meet them, they had to also had travelled "d" miles.
now the robbers by then have been travelling for "t" minutes, and the cops were at the donut shop eating, they got the call and took off 30 minutes later, so by the time the cops catch up with them, the cops haven't travelled "t" minutes, they have been travelling less than that, 30 minutes less due to the delay from the call, so the cops have been going for "t-30" minutes.
and we know their rates.
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{minutes}{time}\\ &------&------&------\\ crooks&d&66&t\\ cops&d&132&t-30 \end{array} \\\\\\ \begin{cases} \boxed{d}=66t\\ d=132(t-30)\\ ----------\\ \boxed{66t}=132(t-30) \end{cases} \\\\\\ 66t=132t-396\implies 396=66t\implies \cfrac{396}{66}=t\implies 6=t[/tex]
now, bear in mind that, for the police to overtake the robbers, they must first meet, and then overtake them.... well, clearly the cops don't want to overtake them, they want to arrest them, so if they just pass by the robbers, not much there, but anyway.
if the robbers had travelled a "d" miles, when the cops meet them, they had to also had travelled "d" miles.
now the robbers by then have been travelling for "t" minutes, and the cops were at the donut shop eating, they got the call and took off 30 minutes later, so by the time the cops catch up with them, the cops haven't travelled "t" minutes, they have been travelling less than that, 30 minutes less due to the delay from the call, so the cops have been going for "t-30" minutes.
and we know their rates.
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{minutes}{time}\\ &------&------&------\\ crooks&d&66&t\\ cops&d&132&t-30 \end{array} \\\\\\ \begin{cases} \boxed{d}=66t\\ d=132(t-30)\\ ----------\\ \boxed{66t}=132(t-30) \end{cases} \\\\\\ 66t=132t-396\implies 396=66t\implies \cfrac{396}{66}=t\implies 6=t[/tex]
