PROBLEM:
My Ford Bronco was fitted at the factory with 30 inch diameter
tires. That means its speedometer is calibrated for 30 inch diameter
tires. I "enhanced" the vehicle
with All Terrain tires that have a 31 inch diameter. How will
this change the speedometer readings? Specifically, assuming the
speedometer was accurate in the
first place, what should I make the speedometer read as I drive
with my 31 inch tires so that the actual speed is 55 mph?
Forego the discussion of whether it is safe to drive a Bronco that fast . . .
One would expect some use of ratios here . . .
Solution:
This problem was the easiest of all for me to solve. Working with ratios (or fractions) is right up my alley! Now fractions working with my sixth and seventh graders...well...that's a totally different story.
First, I set up the ratio (or proportion):
This means that with 30 inch diameter tires, I will be driving 55 miles per hour, and with 31 inch diameter tires, I would travel approximately 57 miles per hour.
Second, I looked at interchanging the ratios so that you are actually going 55 miles per hour with 31 inch diameter tires. This is what my outcome was:
When I interchanged my ratios to set 31 inch tires to a 55 mile per hour speed limit, 30 inch tires would travel approximately 53 miles per hour.
In order for my kids to appreciate how much faster the Bronco will go, they can get involved with creating a spreadsheet to see how the rates will change. Click here to see for yourself!