the truck must be rented for hours before the cost under the new plan becomes $20 more expensive than the old plan
Let's assume that the cost of renting the truck for 1 hour under the old plan is $x per hour.
Therefore, under the new plan, the cost of renting the truck for 1 hour would be $x + $20.
Let's represent the number of hours the truck must be rented for under the new plan as 'h'.
According to the given condition, the cost under the new plan becomes $20 more expensive than the old plan after 'h' hours.
Therefore, the equation representing this condition can be written as:
$h(x + $20) = hx + $20
Simplifying the equation:
$hx + $20h = hx + $20
$20h = $20
h = 1
So, the truck must be rented for 1 hour before the cost under the new plan becomes $20 more expensive than the old plan.
To find the number of hours the truck must be rented for before the cost under the new plan becomes $20 more expensive than the old plan, we'll need to set up an equation.
Let's assume the cost of renting the truck per hour under the old plan is represented by O hours and the cost under the new plan is represented by N hours.
According to the given information, the cost under the new plan becomes $20 more expensive than the old plan after renting for a certain number of hours. Mathematically, this can be expressed as:
N hours = O hours + $20
Now, we need to solve for N, which represents the number of hours the truck must be rented for under the new plan.
Let's assume the truck must be rented for X hours before the cost under the new plan becomes $20 more expensive than the old plan. Substituting X for N in the equation, we have:
X = O + $20
Therefore, the truck must be rented for X hours (or the number of hours we solve for) before the cost under the new plan becomes $20 more expensive than the old plan.