MATH SOLVE

2 months ago

Q:
# 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 milesb.1328 milesc.1500 milesd.1592 miles

Accepted Solution

A:

Answer:Option d.1592 milesStep-by-step explanation:step 1Find out the circumference for the original diameter of the tireThe 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 tireFind out the number of revolutions of the tire for a distance of 1,500 miles1,500/(76.93/63,360)=1,235,408.81 revstep 2Find out the circumference for the new diameter of the tireThe 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 Methodwe know thatThe 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 distanceso[tex]\frac{26}{24.5}(1,500)=1591.8\ miles[/tex]Round to the nearest whole number[tex]1592\ miles[/tex]