Answer:
b. 4:35 p.m
Step-by-step explanation:
Her speed in t minutes after 4:30 p.m. is modeled by the following equation:
[tex]v(t) = v(0) + at[/tex]
In which v(0) is her speed at 4:30 pm and a is the acceleration.
At 4:30 p.m. she looks down at her speedometer and notices that she is going 45 mph.
This means that [tex]v(0) = 45[/tex]
Ten minutes later she looks down at the speedometer again and notices that she is going 55 mph.
This means that [tex]v(10) = 55[/tex]
So
[tex]v(t) = v(0) + at[/tex]
[tex]55 = 45 + 10a[/tex]
[tex]10a = 10[/tex]
[tex]a = 1[/tex]
So
[tex]v(t) = 45 + t[/tex]
When was she moving exactly 50 mph?
This is t minutes after 4:30 p.m.
t is found when v(t) = 50. So
[tex]v(t) = 45 + t[/tex]
[tex]50 = 45 + t[/tex]
[tex]t = 5[/tex]
5 minutes after 4:30 p.m. is 4:35 p.m.
So the correct answer is:
b. 4:35 p.m
