SOLUTION: A truck passes a highway patrol station going 70 km/hr. When the truck is 10 kilometers past the station, a patrol car starts after it going 100 km/hr. Let t be the number of hours

Algebra ->  Test -> SOLUTION: A truck passes a highway patrol station going 70 km/hr. When the truck is 10 kilometers past the station, a patrol car starts after it going 100 km/hr. Let t be the number of hours      Log On


   

Question 788059: A truck passes a highway patrol station going 70 km/hr. When the truck is 10 kilometers past the station, a patrol car starts after it going 100 km/hr. Let t be the number of hours the patrol car has been going.
a) What expression represents the patrol car's distance from the station? What expression represents the trucks distanxe from the station after t hours?
b) When does the patrol car catch the truck?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
t= number of hours the patrol car has been going.
a) What expression represents the patrol car's distance from the station?
100%2At=100t= patrol car's distance from the station, in km.
What expression represents the truck's distance from the station after t hours?
The truck was 10 km past the station at t=0 (when the patrol car started the chase), so
10%2B70%2At=70t%2B10= truck's distance from the station t hours after the patrol car starts chasing it.
b) When does the patrol car catch the truck?
When they at at the same distance from the station, the solution to the equation
100t=70t%2B10
Solving:
100t=70t%2B10-->100t-70t=70t%2B10-70t-->%28100-70%29t=10-->30t=10-->t=10%2F30-->t=1%2F3
The patrol car catches the truck after 1%2F3 of an hour, which is
%281%2F3%29%2A%2860minutes%29=20minutes

PS_ What I do not understand is why the patrol car was chasing the truck. 70 km/h is only about 45 miles per hour, and that is not too fast for a highway.