Economy Movers charge $85 plus $40 an hour to move households across town. Helpful Moving Company charges $60 an hour for cross-town moves. For what lengths of time is Helpful Moving Company more expensive?

I'm sure there's an algebraic method of determining this.

However, trial and error will also get the answer.

85 + 40 = 125
85 + 80 = 165
85 + 120 = 205
85 + 160 = 245

60
120
180
240

A= Total charges of Economy Movers in t hours.

B= Total charges of Helpful Moving Company in t hours.

Write an inequality B>A to determine t.

To determine for what lengths of time Helpful Moving Company is more expensive than Economy Movers, we need to compare the costs of both companies for different time durations.

Let's assume we are considering a time duration of "x" hours.

For Economy Movers:
They charge a fixed fee of $85 plus an additional $40 per hour. So, their cost can be represented as:
Cost of Economy Movers = $85 + ($40 * x)

For Helpful Moving Company:
They charge $60 per hour for cross-town moves, so their cost can be represented as:
Cost of Helpful Moving Company = $60 * x

Now, we can set up an equation to find the point at which the costs are equal:
$85 + ($40 * x) = $60 * x

Let's solve this equation:

$85 + $40x = $60x
$85 = $60x - $40x
$85 = $20x
x = $85 / $20
x = 4.25

Therefore, it is when the time duration is more than 4.25 hours that Helpful Moving Company becomes more expensive than Economy Movers. For any duration less than 4.25 hours, Economy Movers is the more expensive option.