When the middle car catches the lead car

Three cars travel the same way along a single-lane road, each at its own constant speed. At one moment Alice is $d$ behind Bob, and Carter is $2d$ ahead of Bob. Seven minutes later Alice overtakes Bob, and five minutes after that she overtakes Carter. How many seconds after Alice passes Carter does Bob pass Carter?

400. Using relative speeds, $v_A-v_B=d/7$ and $v_A-v_C=3d/12=d/4$ per minute, so $v_B-v_C=d/4-d/7=3d/28$. Bob closes the $2d$ gap in $\tfrac{2d}{3d/28}=\tfrac{56}{3}$ minutes, which is $6$ min $40$ s after Alice's pass at minute $12$, i.e. $400$ seconds.