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
[tex]C=\pi D[/tex]
we have
[tex]D=24.5\ in[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]C=(3.14)(24.5)=76.93\ in[/tex]
[tex]1\ mile=63,360\ inches[/tex]
[tex]76.93\ in=76.93/63,360\ mi[/tex]
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
[tex]C=\pi D[/tex]
we have
[tex]D=26\ in[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]C=(3.14)(26)=81.64\ in[/tex]
[tex]81.64\ in=81.64/63,360\ mi[/tex]
Multiply by the number of revolutions in step 1
[tex](81.64/63,360)1,235,408.81=1591.8\ mi[/tex]
Round to the nearest whole number
[tex]1592\ miles[/tex]
Alternative Method
we know that
The ratio of the diameters of the tires is equal to the scale factor
[tex]\frac{26}{24.5}[/tex]
To find out the new distance, multiply the scale factor by the original distance
so
[tex]\frac{26}{24.5}(1,500)=1591.8\ miles[/tex]
Round to the nearest whole number
[tex]1592\ miles[/tex]
