Answer:
Total Distance = 2 miles
Step-by-step explanation:
We know D = RT where
D is distance
R is rate (speed)
T is time
First Leg:
Rate = x mph
Time = 20/60 = 1/3 hour
Hence, D = RT, Distance = x * 1/3 = x/3 miles
Second Leg:
Rate = x - 1
Time = 30/60 = 1/2 hour
Distance = (x - 1) * 1/2 = (x-1)/2
Total distance is the sum of both the legs, hence,
Total distance = [tex]\frac{x}{3}+\frac{x-1}{2}=\frac{2x+3(x-1)}{6}=\frac{2x+3x-3}{6}=\frac{5x-3}{6}[/tex] miles
Since both the distance are equal we can equate and solve:
[tex]\frac{x}{3}=\frac{x-1}{2}\\2x=3x-3\\x=3[/tex]
Plugging this x = 3 into the total distance expression, we get:
[tex]\frac{5x-3}{6}\\\frac{5(3)-3}{6}\\=2[/tex]
Total distance, 2 miles
