Radius of a snow tire...

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Hello! I've tried solving this problem using ratios, proportions, and even pi, but I just can't come up with anything that makes sense! Here's the problem:

You travel to the mountains in a car and the tripometer reads 450 miles. On the way home, you take the exact same route but with snow tires on the car. This time, the tripometer reads 440 miles. Find the radius of the snow tire, if the radius of the original tires is 15 inches. (Use exact form)

So, exact form means no rounding, just a fraction/radical etc.... and I've tried 450/15=440/x, but I didn't get anything reasonable... I also tried calculating the circumference of the orignial tire, and comparing that to the new milage... but again no luck. Thanks SO much for any help you can provide!
 
I believe you have it right.

450/15 = 440/x
small tire r=(44/3) inches

Small tire: c = 2(pi)(44/3) = [(1/3)88(pi)] inches around (approx 92.1534 inches in circumference)
Large tire: c = 2(pi)(15) = 30(pi) inches around (approx 94.2478 inches in circumference)

(thats my bit... follow the rest of skeeter)
 
the normal tires registered a distance of 450 miles because of the number of revolutions they made.

the snow tires registered a distance of 440 miles because they made fewer revolutions for the same distance ... therefore, the snow tires have a larger radius.

the result is an inverse proportionality ...

let r = snow tire radius

450/440 = r/15

r = 15.34"
 
jwpaine said:
450/440 = r/15

r = 15.34"
Click to expand...

Skeeter... why not:
450/15 = 440/x
r=(44/3) inches


I tried to help, but obviously I have failed in my attempt :(
Click to expand...
44/3 is about 14.6666 inches, which is less than 15, and since the
Thanks for your help... that's how I did it too, but that can't be right, because 44/3 is about 14.6666 inches, which is less than 15, and since the snow tires were larger... :) That's all I knew... I think Skeeter's way sort of made sense, I never thought about an inverse proportion...
 
ArcainineFalls531 said:
You travel to the mountains in a car and the tripometer reads 450 miles. On the way home, you take the exact same route but with snow tires on the car. This time, the tripometer reads 440 miles. Find the radius of the snow tire, if the radius of the original tires is 15 inches.
Click to expand...
I must be dense, cause that makes no sense to me.
How can tire size "shorten" a distance? Like, how can SAME ROUTE be 450 and 440?

On the way home with the larger tires, the distance is still 450...unless someone
moved the home 10 miles!

The only difference is the larger tires mean less revolutions.
If you travel 1 mile with circumference of tires = 3.3 feet,
then the tires made 5280 / 3.3 = 1600 revolutions.
If you put on larger tires and the revolutions for a mile = 1500,
then circumference of larger tires = 5280 / 1500 = 3.52 feet.
 
Denis said:
ArcainineFalls531 said:
You travel to the mountains in a car and the tripometer reads 450 miles. On the way home, you take the exact same route but with snow tires on the car. This time, the tripometer reads 440 miles. Find the radius of the snow tire, if the radius of the original tires is 15 inches.
Click to expand...
I must be dense, cause that makes no sense to me.
How can tire size "shorten" a distance? Like, how can SAME ROUTE be 450 and 440?

On the way home with the larger tires, the distance is still 450...unless someone
moved the home 10 miles!

The only difference is the larger tires mean less revolutions.
If you travel 1 mile with circumference of tires = 3.3 feet,
then the tires made 5280 / 3.3 = 1600 revolutions.
If you put on larger tires and the revolutions for a mile = 1500,
then circumference of larger tires = 5280 / 1500 = 3.52 feet.
Click to expand...
Denis,

The miles traveled isn't what changes, it's the miles read on the tripometer of the car that shows 10 fewer miles. This makes sense, because the bigger tires do make fewer revolutions, which shows fewer miles on the car. The thing I'm trying to calculate is the radius of the bigger tires.... Thanks! :)
 
Clarifying note: A car's odometer is set to calculate distance according to rotations of the axle, and assumes a certain tire radius.

Changing the tire size obviously won't change the distance between towns, but it will change the odometer's perception of the distance, since a revolution will now measure a different distance from what the odometer is set for.

Eliz.

How Stuff Works: How Odometers Work
 
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