The sign shows distances from a rest stop to the exits for different towns along a straight section of highway. The state department of transportation is planning to bulld a new exit to Freestone at the midpoint of the exits for Roseville and Edgewood. When the new exlt is built, what will be the distance from the exit for Midtown to the exit for Freestone?

Question

midtown - 17 mi.
roseville - 37 mi.
edgewood - 59 mi.

When the new exit is built the distance from the exit for Midtown to the exit for Freestone will be _____ miles

Answer 1

To find the distance from the new exit for Freestone to the exit for Midtown, we first need to determine the midpoint between the exits for Roseville and Edgewood.

1. Distances:

   • Midtown: 17 miles
   • Roseville: 37 miles
   • Edgewood: 59 miles

2. Midpoint Calculation: The midpoint between Roseville and Edgewood is calculated by taking the average of the distances: \[ \text{Midpoint} = \frac{\text{Distance to Roseville} + \text{Distance to Edgewood}}{2} = \frac{37 + 59}{2} \] \[ \text{Midpoint} = \frac{96}{2} = 48 \text{ miles} \] So the exit for Freestone will be at 48 miles from the rest stop.

3. Distance from Midtown to Freestone: Now, we calculate the distance from Midtown (17 miles) to the new exit for Freestone (48 miles): \[ \text{Distance from Midtown to Freestone} = 48 - 17 = 31 \text{ miles} \]

Therefore, when the new exit is built, the distance from the exit for Midtown to the exit for Freestone will be 31 miles.