Question 788059
{{{t}}}= number of hours the patrol car has been going.
a) What expression represents the patrol car's distance from the station?
{{{100*t=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+70*t=70t+10}}}= 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+10}}}
Solving:
{{{100t=70t+10}}}-->{{{100t-70t=70t+10-70t}}}-->{{{(100-70)t=10}}}-->{{{30t=10}}}-->{{{t=10/30}}}-->{{{t=1/3}}}
The patrol car catches the truck after {{{1/3}}} of an hour, which is
{{{(1/3)*(60minutes)=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.