Question

Aaron had a Suburban with oversized tires. The original tires designed for the Suburban had a diameter of 724.9 mm. The actual tires have a diameter of 750.9 mm. The Suburban’s odometer (based on the original tire size) reads that Aaron drove 200,000 miles in the car. If the suburban had the larger tires installed at 50,000 miles, how far has the Suburban actually driven?

Answer 1

For the original tires, we have

C_original = 2r

C_original = 2 (3.14) [(724.9 x 10^-3 m) / 2]

C_original = [(6.28) (362.45 x 10^-3 m)]

C_original = 2.27 m

For the actual tires, we have

C_actual = 2R

C_actual = 2 (3.14) [(750.9 x 10^-3 m) / 2]

C_actual = [(6.28) (375.45 x 10^-3 m)]

C_actual = 2.35 m

Distance traveled by the Suburban’s with actual tires than the Suburban’s with original tires which will be given as -

d = C_actual - C_original

d = [(2.35 m) - (2.27 m)]

d = 0.08 m

Then, we have

N = [(2.35 m) / (2.27 m)]

N = 1.03 times

The Suburban’s actual tires has traveled 1.03 times further than the Suburban’s with original tires.

If the Suburban had the larger tires installed at 50,000 miles, how far has the Suburban actually driven?

Distance = [(1.03) (50,000 miles)]

Distance = 51500 miles