Answer:
Her usual driving speed is 38 miles per hour.
Step-by-step explanation:
We know that:
[tex]s = \frac{d}{t}[/tex]
In which s is the speed, in miles per hour, d is the distance, in miles, and t is the time, in hours.
We have that:
At speed s, she takes two hours to drive. So
[tex]s = \frac{d}{2}[/tex]
[tex]d = 2s[/tex]
However, on one particular trip, after 40% of the drive, she had to reduce her speed by 30 miles per hour, driving at this slower speed for the rest of the trip. This particular trip took her 228 minutes.
228 minutes is 3.8 hours. So
[tex]0.4s + 0.6(s - 30) = \frac{d}{3.8}[/tex]
So
[tex]3.8(0.4s + 0.6s - 18) = d[/tex]
[tex]3.8s - 68.4 = 2s[/tex]
[tex]1.8s = 68.4[/tex]
[tex]s = 38[/tex]
Her usual driving speed is 38 miles per hour.
