I'm only going to give a hint to this problem. The rest you should be able to finish yourself.
So we need two equations here, one representing the total hours from each driving zone and one representing the amount of miles covered in each zone. Our two zone will be traffic which we will call x and clear which will be y. The variables will represent the amount of hours in those zones.
The first equation to represent the total hours traveled is:
x+y=7. Simple enough. We spend x hours in traffic and y hours on the clear road for a total of 7.
The second equation to represent the total miles traveled is:
19x+54y=238. Since multiplying the variables and speeds together yields only the unit of miles (i.e. (miles/hour)*hour, the hour cancels out) then in the end we will have 19x amount of miles in traffic and 54y miles on the clear road for a total of 238 miles.
Here's the hint that will help you solve this: You need to solve one of these equations for either the x or y variable and use that to plug into the other equation and solve it for the remaining variable. Example:
We solve for x in the first equation and plug in that x value into the second, we will then solve for the y variable. After getting the y variable we can plug that back into either equation to get the x.
Hope this helped. Maybe someone else will write up the precise answer.
1/15/2013

Mykola V.