finding distance between 2 points on a circle

Question

1. To make getting to BWI easier, we are going to use a shuttle service. Due to an accident on I-195, we will get on the Baltimore Beltway (I-695) at Exit 12B, Wilkins Avenue and take it to Exit 7, the Baltimore Washington Parkway (MD 295). Assuming the Beltway is a perfect circle with a radius of 7.79 miles, and the angle between Exit 7 and Exit 12B is 0.513 radians:
a. Find the distance we traveled on the beltway. (Draw relevant diagram.)
b. If our average driving speed was 59 mph, how long did it take us to travel from Exit 7 to Exit 12B?

Answer 1

a. The arc length, s, along a circle of radius r is given by s = rθ, where θ is the radian measure of the central angle that cuts off the arc.

 

    s = rθ = (7.79)(0.513) ≈ 4 miles

 

b. Distance = (Rate)(Time), so Time = Distance/Rate

 

                                                   = 4/59 = 0.068 hr = 4.07 minutes