The time to drive from Denver to Boulder at 30 MPH takes D/30 hours, where D is the distance.
Similarly, the drive from Boulder to Denver at 45 MPH takes D/45 hours.
The round trip, therefore takes
D/30 + D/45 hours.
The LCD is 90, so we will multiply the first fraction by 3/3 and the second by 2/2, giving
3D/90 + 2D/90 = 5D/90.
But this simplifies to D/18.
We know that the round trip took 1.75 hours. This gives the equation:
D/18 = 1.75 Multiply both sides by 18.
D = 18 * 1.75 = 31.5