A boat company charges a flat fee of $35.00 plus $7.25 per hour to rent a boat. Another company charges a fee of $29.00 plus $10.50 per hour to rent the same boat. Find the number of hours for which the costs are the same. Round your answer to the nearest whole hour.
35.00 + 7.25x = 29.00 + 10.50x
To find the number of hours for which the costs are the same, we need to set up and solve an equation.
Let's denote the number of hours as "h".
For the first company, the cost of renting the boat can be expressed as:
Cost1 = $35.00 + $7.25 * h
For the second company, the cost of renting the boat can be expressed as:
Cost2 = $29.00 + $10.50 * h
To find the number of hours for which the costs are the same, we can set up the equation:
Cost1 = Cost2
$35.00 + $7.25 * h = $29.00 + $10.50 * h
Now, we can solve this equation to find the value of "h".
Subtract $29.00 from both sides of the equation:
$35.00 + $7.25 * h - $29.00 = $10.50 * h
Combine like terms:
$6.00 + $7.25 * h = $10.50 * h
Subtract $7.25 * h from both sides of the equation:
$6.00 = $10.50 * h - $7.25 * h
Combine like terms:
$6.00 = $3.25 * h
Now, divide both sides of the equation by $3.25 to solve for "h":
$6.00 / $3.25 = h
Approximately:
h ≈ 1.846, or rounded to the nearest whole number, h = 2
So, the costs for both companies will be the same after approximately 2 hours of renting the boat.