Answer:
Option d.1592 miles
Step-by-step explanation:
step 1
Find out the circumference for the original diameter of the tire
The circumference is equal to
![C=\pi D](https://tex.z-dn.net/?f=C%3D%5Cpi%20D)
we have
![D=24.5\ in](https://tex.z-dn.net/?f=D%3D24.5%5C%20in)
assume
![\pi =3.14](https://tex.z-dn.net/?f=%5Cpi%20%3D3.14)
substitute
![C=(3.14)(24.5)=76.93\ in](https://tex.z-dn.net/?f=C%3D%283.14%29%2824.5%29%3D76.93%5C%20in)
![1\ mile=63,360\ inches](https://tex.z-dn.net/?f=1%5C%20mile%3D63%2C360%5C%20inches)
![76.93\ in=76.93/63,360\ mi](https://tex.z-dn.net/?f=76.93%5C%20in%3D76.93%2F63%2C360%5C%20mi)
The circumference represent the distance of one revolution of the tire
Find out the number of revolutions of the tire for a distance of 1,500 miles
1,500/(76.93/63,360)=1,235,408.81 rev
step 2
Find out the circumference for the new diameter of the tire
The circumference is equal to
![C=\pi D](https://tex.z-dn.net/?f=C%3D%5Cpi%20D)
we have
![D=26\ in](https://tex.z-dn.net/?f=D%3D26%5C%20in)
assume
![\pi =3.14](https://tex.z-dn.net/?f=%5Cpi%20%3D3.14)
substitute
![C=(3.14)(26)=81.64\ in](https://tex.z-dn.net/?f=C%3D%283.14%29%2826%29%3D81.64%5C%20in)
![81.64\ in=81.64/63,360\ mi](https://tex.z-dn.net/?f=81.64%5C%20in%3D81.64%2F63%2C360%5C%20mi)
Multiply by the number of revolutions in step 1
![(81.64/63,360)1,235,408.81=1591.8\ mi](https://tex.z-dn.net/?f=%2881.64%2F63%2C360%291%2C235%2C408.81%3D1591.8%5C%20mi)
Round to the nearest whole number
![1592\ miles](https://tex.z-dn.net/?f=1592%5C%20miles)
<em>Alternative Method</em>
we know that
The ratio of the diameters of the tires is equal to the scale factor
![\frac{26}{24.5}](https://tex.z-dn.net/?f=%5Cfrac%7B26%7D%7B24.5%7D)
To find out the new distance, multiply the scale factor by the original distance
so
![\frac{26}{24.5}(1,500)=1591.8\ miles](https://tex.z-dn.net/?f=%5Cfrac%7B26%7D%7B24.5%7D%281%2C500%29%3D1591.8%5C%20miles)
Round to the nearest whole number
![1592\ miles](https://tex.z-dn.net/?f=1592%5C%20miles)