My trip to work is 120 miles. if i go 8 mph faster than my usual speed, i'll get to work 30 minutes earlier. how long does my trip take, in hours, if i go my usual speed?

Let x be the time it takes for the trip to be completed given that the speed is y.

When the time is 30 minutes (equal to 0.5 hour) shorter than x, the speed is 8 mph more than the original speed.

The equations that would best represent the given conditions are:

(1) 120 = (x) (y)

(2) 120 = (x - 0.5) (y + 8)

Simplifying,

y = 120/x

Substitute:

120 = (x - 0.5) (120/x + 8)

The value of x from the equation is 3. Thus, if I go with the usual speed, the time it will take me to finish the trip is approximately 3 hours.