Given the distance 20 miles and the fact that if she drives 10 miles per hour faster, it takes her 4 minutes less to travel the distance, Nancy's new speed is 60 miles per hour.
The relation between distance and speed is given below:
s = v . t
Where:
s = distance
v = velocity or speed
t = time
In the given problem, let:
v = first speed
t = first time periods needed to travel 20 miles, in minutes
s = distance = 20 miles
Her new speed and new time is (v + 10) and (t - 4)
Hence,
v . t / 60 = 20, or
vt = 1200
v = 1200/t
After increasing the speed, the following holds:
(v + 10) (t - 4)/60 = 20
vt + 10t - 4v - 40 = 1200
Substitute vt = 1200 and v = 1200/t
10t - 4800/t - 40 = 0
Multiply by t/10
t² - 4t - 480 = 0
(t - 24) (t+20) = 0
t = 24 or t = -20
Therefore, the time that satisfies the equation is t = 24 minutes.
Her original speed is:
v = 1200/t = 1200/24 = 50 miles per hour
Her new speed is:
v + 10 = 50 + 10 = 60 miles per hour
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