Alright, let's go through the problem step-by-step to understand how fast the car owner is actually traveling when the speedometer reads 70 mph after changing the tires.
1. Understand the Original and New Tire Diameters:
- The original tires have a diameter of 24.8 inches.
- The new tires have a diameter of 26.8 inches.
2. Speedometer Speed:
- The speedometer reads 70 miles per hour (mph).
3. Calculating the Ratio of Diameters:
- To figure out how the new tire size affects the actual speed, we first calculate the ratio of the new tire diameter to the original tire diameter.
- The ratio is given by [tex]\( \text{diameter ratio} = \frac{\text{new diameter}}{\text{original diameter}} \)[/tex].
4. Performing the Calculation for the Diameter Ratio:
- Plugging in the values:
[tex]\[
\text{diameter ratio} = \frac{26.8 \text{ inches}}{24.8 \text{ inches}} = 1.0806451612903225
\][/tex]
5. Calculating the Actual Speed:
- To find the actual speed, we multiply the speedometer reading by the diameter ratio:
[tex]\[
\text{actual speed} = 70 \text{ mph} \times 1.0806451612903225 = 75.64516129032258 \text{ mph}
\][/tex]
6. Rounding the Actual Speed:
- Finally, we round the actual speed to two decimal places:
[tex]\[
\text{actual speed (rounded)} = 75.65 \text{ mph}
\][/tex]
So, when the speedometer reads 70 mph, the car owner is actually traveling at approximately 75.65 mph.
