Question

If you have changed the tires on your car, the original diameter is 24.5 inches, to a new diameter of 26 inches, how far have you actually gone if your odometer is reading 1500 miles?
a.1226 miles
b.1328 miles
c.1500 miles
d.1592 miles​

Answer 1

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

$C=\pi D$

we have

$D=24.5\ in$

assume

$\pi =3.14$

substitute

$C=(3.14)(24.5)=76.93\ in$

$1\ mile=63,360\ inches$

$76.93\ in=76.93/63,360\ mi$

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

$C=\pi D$

we have

$D=26\ in$

assume

$\pi =3.14$

substitute

$C=(3.14)(26)=81.64\ in$

$81.64\ in=81.64/63,360\ mi$

Multiply by the number of revolutions in step 1

$(81.64/63,360)1,235,408.81=1591.8\ mi$

Round to the nearest whole number

$1592\ miles$

Alternative Method

we know that

The ratio of the diameters of the tires is equal to the scale factor

$\frac{26}{24.5}$

To find out the new distance, multiply the scale factor by the original distance

so

$\frac{26}{24.5}(1,500)=1591.8\ miles$

Round to the nearest whole number

$1592\ miles$