Acme Movers charges $280 plus $40 per hour to move household goods across town. Hank's Movers charges $75 per hour. For what lengths of time does it cost less to hire Hank's Movers?
It costs less to hire Hank's Movers for times less than
how many hours
75x < 280+40x
To find out for what lengths of time it costs less to hire Hank's Movers, we need to compare the costs of both movers.
Let's assume x represents the number of hours required to move household goods across town.
For Acme Movers:
Cost = $280 + $40 per hour
Cost = $280 + $40x
For Hank's Movers:
Cost = $75 per hour
Cost = $75x
To determine for what lengths of time it costs less to hire Hank's Movers, we need to identify when the cost of Hank's Movers is less than the cost of Acme Movers. In other words, we want to find when the equation Hank's Movers cost < Acme Movers cost.
$75x < $280 + $40x
Now, let's solve this inequality to find the range of values for x where Hank's Movers cost less:
$75x - $40x < $280
$35x < $280
x < $280 / $35
x < 8
Therefore, for lengths of time less than 8 hours, it costs less to hire Hank's Movers.