Problem: Big Tires (click here for a statement of the problem)

My Solution.

We can express RATE
as a ratio between DISTANCE travelled and the TIME it takes to travel that distance.

In the case of the affect of tire size on the speedometer reading, we need to consider a ratio between the RATES:




We can also look at this problem as related to the ratio between the CIRCUMFERENCES of the tires. Recall that CIRCUMFERENCE can be expressed by the relationship:


where r is the RADIUS and d is the DIAMETER



The ratio between the CIRCUMFERENCE of the original tires and the replacement tires is:






So either way, the problem is reduced to the ratio between the DIAMETERS of the tires:





Multiplying the ratio by 55mph:


That is to say, when the speedometer reads 53mph, the actual speed of the truck is 55mph.