Sure! Let's write a system to find the number of hours in which the total charge will be the same for both lawn mower services.
Let's define the total charge function for each service:
For the first lawn mower service:
Total Charge 1 = Service Fee 1 + (Hourly Rate 1 * Number of Hours)
For the second lawn mower service:
Total Charge 2 = Service Fee 2 + (Hourly Rate 2 * Number of Hours)
We want to find the number of hours when the total charges for both services are equal. So, we'll set up an equation:
Service Fee 1 + (Hourly Rate 1 * Number of Hours) = Service Fee 2 + (Hourly Rate 2 * Number of Hours)
Now, let's substitute the given values into the equation:
$45 + ($20 * Number of Hours) = $30 + ($26 * Number of Hours)
We can simplify this equation:
$45 + $20 * Number of Hours = $30 + $26 * Number of Hours
By moving all the terms with Number of Hours to one side of the equation and the remaining terms to the other side, we get:
$20 * Number of Hours - $26 * Number of Hours = $30 - $45
Simplifying further:
($20 - $26) * Number of Hours = $30 - $45
$(-$6) * Number of Hours = -$15
Dividing both sides by -$6:
Number of Hours = -$15 / -$6
Number of Hours = 2.5
According to the calculation, the number of hours in which the total charge will be the same for both lawn mower services is 2.5 hours.
Please note that it's not possible to have half an hour, so in practice, you would likely round up to the nearest whole number of hours.