Question 515194
Let s be the average speed of the car.

Since the bus is traveling 11 mph slower than the car, we can express the average speed of the bus as {{{s - 11}}}.

The relationship between distance traveled, average speed, and time is:

Distance Traveled = (Average Speed)(Time)

Therefore, after 4.25 hours, the car has traveled

Distance Traveled by Car = {{{(s)(4.25) = 4.25s}}} miles

while the bus has traveled

Distance Traveled by Bus = {{{(s - 11)(4.25) = 4.25s - 46.75}}} miles (distributing the 4.25 in the last step)

We know that the car and the bus are traveling in opposite directions, and that the distance between them after 4.25 hours is 174 miles.  We can express this fact algebraically as an equation:

Distance Traveled by Car + Distance Traveled by Bus = 174
{{{4.25s + 4.25s - 46.75 = 174}}}

Now we solve for s:

{{{8.50s - 46.75 = 174}}} (combine like terms)
{{{8.50s = 220.75}}} (add 46.75 to both sides)
{{{ s = 220.75/8.50 }}} (divide both sides by 8.50)

So we get that the average speed of the car is {{{220.75/8.50}}} mph, or, to the nearest hundredth, 25.97 mph.  Does this make sense?  If the car is traveling at {{{220.75/8.50}}} mph, after 4.25 hours it will have traveled {{{(220.75/8.50)(4.25) = 110.375 miles.  The bus is traveling 11 mph slower, or (to the nearest hundredth:

{{{220.75/8.50 - 11 = 14.97}}} mph

After 4.25 hours then, the bus has traveled:

{{{(220.75/8.50 - 11)*4.25 = 63.625}}} miles

Therefore the car and the bus will be 110.375 + 63.625 = 174 miles apart after 4.25 hours, so our solution works.