【Question 12】
A bicycle tire, if installed on the front wheel, will wear out after the bicycle has traveled 5000 kilometers; if installed on the rear wheel, it will wear out after the bicycle has traveled 3000 kilometers. If the front and rear tires are swapped after a certain distance, and both the front and rear tires are worn out at the same time, then the bicycle can travel $\qquad$ kilometers.
【Analysis and Solution】
Every $15000$ kilometers driven, 
the front tires wear out $15000 \div 5000=3$ units, and the rear tires wear out $15000 \div 3000=5$ units, totaling $3+5=8$ units; so a pair of tires (2 units) can travel at most $15000 \div(8 \div 2)=3750$ kilometers.

That is, when $3750 \div 2=1875$ kilometers have been driven, the front and rear tires should be swapped; then they will both wear out exactly at 3750 kilometers.