A car is driven 50,000 miles. Its 5 tires (one is the spare)are rotated
regularly and frequently. How many miles will any one tire have travelled on
the road by the end of the trip?
There are 50,000 x 4 or 200,000 tire miles in a 50,000 mile trip.
If the 200,000 tire miles are shared equally by the 6 tires for
the entire 50,000 miles, then we divide 200,000 by 5 and each tire's
share of the total 200,000 tire miles, and each tire will be driven
40,000 miles.
This is probably the answer your teacher is expecting.
However, technically there isn't enough information given to solve the
problem. You'd have to be given how many miles the car is driven before
the tires are rotated.
The above figure of 40,000 miles each would be exactly correct only if
the tires are rotated every n miles where n divides evenly into 10000.
In all other cases the answer will be different.
Look at these cases:
If they are rotated only once every 50,000 miles (or less often), the spare
will never get used, and the 4 on the ground will each go 50,000 miles.
If they are rotated every 40,000 miles then 3 of the tires will be used 50000
miles, one will be used 40,000 and one will be used only 10,000
If they are rotated every 30,000 miles then 3 of the tires will be used 50000
miles, and the other one will be used 30,000 miles, and one 20,000.
If they are rotated every 20,000 miles then 2 of the tires will be used 50000
miles, one will be used 40,000 miles and the other two will be used only 30,000
miles.
You should point this out to your teacher.
Suppose, for example, they are rotated every 12,000 miles, Then for
0 - 12000 miles, tires 1,2,3,4 each travel 12000 mi and tire 5 travels 0
12000 - 24000 miles, tires 2,3,4,5 each travel 12000 mi and tire 1 travels 0
24000 - 36000 miles, tires 1,3,4,5 each travel 12000 mi and tire 2 travels 0
36000 - 48000 miles, tires 1,2,4,5 each travel 12000 mi and tire 3 travels 0
48000 - 50000 miles, tires 1,2,3,5 each travel 2000 mi and tire 4 travels 0
So tires 1, 2, 3, and 5 have each traveled 38000 miles, tire 4 has traveled
48000 miles.
Edwin
