Question 1110910
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I didn't check all of tutor theo's analysis, but his process seems right and so his answers should be good.<br>
It is easy to show that his answers for parts b and c are right.<br>
A speedometer determines the car's speed by counting the revolutions of the axle.  It shows the correct speed if the tires being used are the ones for which the speedometer was calibrated.<br>
If you put on larger tires, the circumference of the tire is larger, so you go farther on each revolution, so your speed is higher than what the speedometer shows; if you put on smaller tires, you speed is lower than what the speedometer shows.<br>
Since the ratio of the circumferences of two different size tires is the same as the ratio of the diameters, the ratio of actual speed to the speed shown by the speedometer is just the ratio of the diameters.<br>
For part b of the question then...
The diameter of the wheel for which the speedometer is calibrated is 15+2*4.3 = 23.6 inches.  When you put on 5.4 inch tires, the diameter is 15+2*5.4 = 25.8 inches.<br>
If the speedometer shows 65 mph when you are using the larger tires, your actual speed is 65 * (25.8/23.6) = 71.06 mph.<br>
For part c, the new diameter of the wheel is 15+2*3.45 = 21.9 inches.  So when the speedometer reads 30 mph with the smaller tires, your actual speed is 30 *(21.9/23.6) = 27.84 mph.