acme removes charges $100 plus $30 per hour for an across town move. Hanks movers charges $55 per hour. for what lengths of time does it cost less to hire hanks movers

1. Write the cost function for Acme's service:
C(t) = 100 + 30t

2. Write the cost function for Hank's Movers:
H(t) = 55t

3. Set up the inequality \( 55t < 100 + 30t \).

4. Subtract \( 30t \) from both sides to isolate \( t \):
55t - 30t < 100
25t < 100

5. Solve for \( t \) by dividing both sides by 25:
t < 4

So, it costs less to hire Hank's Movers for lengths of time \( t < 4 \) hours.