A jeep and a BMW enter a highway that runs east-west at the same exit heading in opposite directions. The jeep entered the highway 30 minutes before the BMW entered the highway, and traveled 7 mph slower than the BMW. After two hours from the time the BMW entered the highway, the cars were 306.5 miles apart. find the speed of each car, if they were driving on cruise control.

Question

anonymous · Answer

let say $V_B$ is velocity of BMW , so velocity of Jeep is $V_J= V_B -7$
let say the time the BMW leaves the exist is 0, so the time the Jeep leaves the exit is 1/2 hour. That means if the BMW moves in 2hours, the Jeep moves in 2.5 hours
let say after moving in 2.5 hours, the distance between the Jeep and the exit is $D_J = V_j *2=(V_B-7)*2.5$ 
after moving in 2hours, the distance between the BMW and the exit is $D_B = V_B*2$
Since they move in opposite way, the distance between them is d = $D_J+D_B=306.5$
so, we have $(V_B-7)*2.5 + V_B*2=306.5$ 
Solve for $V_B$ then $V_J$

anonymous · Answer

Thank you! That helped.