When the faster driver gains a full lap

Two drivers start together on the same circuit. One completes a lap every $6$ minutes, the other every $9$ minutes. After how many minutes is the faster driver exactly one lap ahead for the first time?

$18$ minutes. The relative speed is $\tfrac16-\tfrac19=\tfrac1{18}$ laps per minute, so gaining one full lap takes $18$ minutes (the faster car has done $3$ laps, the slower $2$).