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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​

User Fxbois
by
8.7k points

1 Answer

0 votes

Answer:

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

User Jon Watte
by
7.9k points
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