There is a mandatory fixed rate of $ 35 that Raphael will have to pay once the service call has been made. This fixed rate is the constant.
The per hour rate is $20. Suppose the machine took "x" hours to get fixed. Then the variable part of the repair cost will be .
Thus, Repair Cost=Fixed Rate Cost+Variable Cost
Or, where
is the total repair cost. Thus, if Raphael ‘s machine took 2 hour to fix, the repair cost is:
dollars.
Therefore, the last option is the correct option.
Answer:
The draining time when only the big drain is opened is 2.303 hours.
The draining time when only the small drain is opened is 5.303 hours.
Step-by-step explanation:
From Physics, we know that volume flow rate (), measured in liters per hour, is directly proportional to draining time (
), measured in hours. That is:
(Eq. 1)
Where is the proportionality constant, measured in liters.
From statement, we have the following three expressions:
(i) <em>Large and small drains are opened</em>
(Eq. 2)
(ii) <em>Only the small drain is opened</em>
(Eq. 3)
(iii) <em>Only the big drain is opened</em>
(Eq. 4)
By applying (Eqs. 3, 4) in (Eq. 2) and making some algebraic handling, we find that:
(Eq. 5)
Whose roots are determined by the Quadratic Formula:
and
Only the first roots offers a solution that is physically reasonable. Hence, the draining time when only the big drain is opened is 2.303 hours. And the time needed for the small drain is calculated by the following formula:
The draining time when only the small drain is opened is 5.303 hours.