Jim travels 6 times as fast as Brenda. Traveling in opposite directions, they are 392 miles apart after 3.5 hours. Find their rates of travel.
Let's set up a system of equations to solve this problem.
Let's say Brenda's rate of travel is x miles per hour.
Jim's rate of travel is then 6x miles per hour.
Traveling in opposite directions, Brenda and Jim cover a combined distance of 392 miles in 3.5 hours.
The rate of travel multiplied by the time traveled gives us the distance traveled.
For Brenda: x * 3.5 = 3.5x
For Jim: 6x * 3.5 = 21x
Their combined distance is then: 3.5x + 21x = 392
Combining like terms gives us: 24.5x = 392
Dividing both sides of the equation by 24.5 gives us: x = 16
Therefore, Brenda's rate of travel is 16 mph and Jim's rate of travel is 6 times faster, so his rate is 6 * 16 = <<6*16=96>>96 mph. Answer: \boxed{16, 96}.