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

Option d.1592 miles​

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

`(26)/(24.5)`

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

so

`(26)/(24.5)(1,500)=1591.8\ miles`

Round to the nearest whole number

`1592\ miles`