let 'x' be the hours needed for moving the household goods across the town

Acme Movers charges $75 plus $20 per hour that is for x hours: 75 + 25x

Hank's Movers charges $45 per hour that is for x hours: 45x

For what lengths of time does it cost less to hire Hank's Movers

Acme Movers cost >= Hank's Movers cost

75 + 25x >= 45x

75 >= 45x - 25x

20x <= 75

x <= 75/20

x <= 3.75 hours

x <= 3 hours 45 minutes

for less then 3.75 hour or 3 hours 45 minutes it costs less to hire Hank's Movers.