Answer:
1.4 hours was in the city.
Step-by-step explanation:
Let [tex]h[/tex] be the amount of time the truck drove on the highway, and [tex]c[/tex] be the amount of time it drove in the city.
Since the total distance the truck traveled was 100 miles, we have
[tex]45h+20c=100[/tex] this says the distances the truck traveled on the highway plus the distance it traveled in the city is 100 miles.
And since the truck traveled for a total of 3 hours, we have:
[tex]h+c=3[/tex]
Thus we have two equations and two unknowns:
(1). [tex]45h+20c=100[/tex]
(2). [tex]h+c=3[/tex]
We solve this system by first solving for [tex]h[/tex] from equation (2) and substituting it into equation (1):
[tex]h=3-c[/tex]
[tex]45(3-c)+20c=100[/tex]
[tex]135-45c+20c=100[/tex]
[tex]135-25c=100[/tex]
[tex]\boxed{c=1.4}[/tex]
the time in the city was 1.4 hours.
And the time on the highway was from equation (2)
[tex]h+1.4=3[/tex]
[tex]\boxed{h=1.6}[/tex]
