Question

donnell rented a trencher for the weekend to dig a trench for a new water line from the county road to his house. the rental charge is given by the equation $c = 125 + 45h$, where $h$ is the number of hours that the trencher runs, based on an internal timer connected to the motor. if the rental charge for the trencher was $840, then how many hours did donnell run the trencher?

hours

Explanation:

Step1: Set up the equation

We know the rental charge \( C = 125 + 45h \) and \( C = 840 \). So we substitute \( C \) with 840 in the equation:
\( 840 = 125 + 45h \)

Step2: Subtract 125 from both sides

To isolate the term with \( h \), we subtract 125 from both sides of the equation:
\( 840 - 125 = 45h \)
\( 715 = 45h \) Wait, no, 840 - 125 is 715? Wait, 840 - 125: 840 - 100 = 740, 740 - 25 = 715? Wait, no, 125 + 45h = 840. So 45h = 840 - 125. 840 - 125 is 715? Wait, no, 840 - 125: 840 - 120 = 720, 720 - 5 = 715. Then divide both sides by 45: \( h=\frac{715}{45}\). Wait, that can't be right. Wait, maybe I made a mistake. Wait, the problem says the rental charge is \( C = 125 + 45h \), and \( C = 840 \). So 125 + 45h = 840. Subtract 125: 45h = 840 - 125 = 715? Wait, 840 - 125: 840 - 100 = 740, 740 - 25 = 715. Then 45h = 715. Then h = 715 / 45. Let's simplify: 715 ÷ 5 = 143, 45 ÷ 5 = 9. So 143/9 ≈15.89? Wait, that seems odd. Wait, maybe the problem was written incorrectly? Wait, maybe the initial charge is 125 and the hourly rate is 45. Wait, maybe I miscalculated. Wait, 125 + 45h = 840. So 45h = 840 - 125 = 715. Then h = 715 / 45 ≈15.89. But that's a fraction. Wait, maybe the rental charge equation was supposed to be \( C = 125 + 45h \), and C is 840. Let me check again. 125 + 45h = 840. Subtract 125: 45h = 715. Divide by 45: h = 715 / 45 = 143/9 ≈15.89. But maybe there's a typo. Wait, maybe the rental charge was $840, and the equation is \( C = 125 + 45h \). Alternatively, maybe the initial charge is 125 and the hourly rate is 45. Wait, maybe I made a mistake in subtraction. 840 - 125: 840 - 125. Let's do 840 - 125: 840 - 100 = 740, 740 - 25 = 715. Yes. Then 45h = 715. So h = 715 / 45 = 15.888... So approximately 15.89 hours. But maybe the problem has a different equation. Wait, maybe the equation is \( C = 125 + 45h \), and C is 840. So solving for h:

\( 125 + 45h = 840 \)

Subtract 125 from both sides:

\( 45h = 840 - 125 \)

\( 45h = 715 \)

Divide both sides by 45:

\( h = \frac{715}{45} = \frac{143}{9} \approx 15.89 \)

But that seems like a strange number. Maybe there's a mistake in the problem statement, or maybe I misread it. Wait, maybe the rental charge is $840, and the equation is \( C = 125 + 45h \). So the answer is \( \frac{143}{9} \) or approximately 15.89 hours. But maybe the problem intended a different number. Wait, maybe the initial charge is 125 and the hourly rate is 45, and the total is 840. So that's the calculation.

Answer:

\( \frac{143}{9} \) (or approximately 15.89) hours