An emergency plumber charges $65 per visit plus an additional $75 per hour. He arrives at Xavien’s house at 9:30 p.m. and works to repair a water leak. The total repair bill Xavien pays is $196.25.Write an equation which can be used to determine the total hours, h, the plumber took to repair the leak.

Question

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What time did the plumber repair the leak?

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Answer 1

To determine the total hours \( h \) the plumber worked, we can set up an equation based on the pricing structure of the plumber.

The plumber charges:

• $65 for the visit (fixed cost)
• $75 per hour (variable cost depending on the time spent)

The total cost can be expressed as: \[ \text{Total Cost} = \text{Visit Fee} + \text{Hourly Rate} \times \text{Hours Worked} \] Substituting the costs into the equation gives us: \[ 196.25 = 65 + 75h \]

Now, we can solve for \( h \):

1. Subtract the visit fee from both sides: \[ 196.25 - 65 = 75h \] \[ 131.25 = 75h \]
2. Now, divide both sides by 75 to isolate \( h \): \[ h = \frac{131.25}{75} \] \[ h = 1.75 \]

So, the total hours \( h \) the plumber took to repair the leak is \( 1.75 \) hours.

Next, to find the time the plumber completed the repair, we can calculate how long \( 1.75 \) hours is from the time he arrived.

He arrived at 9:30 p.m. and worked for \( 1.75 \) hours (which is 1 hour and 45 minutes).

Calculating this:

• 1 hour from 9:30 p.m. brings us to 10:30 p.m.
• Then adding 45 minutes to 10:30 p.m. brings us to 11:15 p.m.

Thus, the plumber finished the repair at 11:15 p.m.

Answer 2

yes but hwta about the equation? you know, it has to be a _h + __ = __

Answer 3

Ah, I see what you're looking for! Let's write the equation in the standard form you mentioned.

Given the breakdown of the costs, we originally derived the equation:

\[ 196.25 = 65 + 75h \]

To express it in the \(h + \text{constant} = \text{constant}\) form, we can rearrange it:

1. Subtract 65 from both sides: \[ 196.25 - 65 = 75h \] \[ 131.25 = 75h \]

2. Now divide both sides by 75 to express \(h\): \[ h = \frac{131.25}{75} \]

However, to create the equation in the form \(h + \text{constant} = \text{constant}\), we can use the original equation and set it as follows:

Starting from: \[ 196.25 = 65 + 75h \]

We can rearrange it: \[ 75h + 65 = 196.25 \]

Thus, the equation you are looking for is: \[ 75h + 65 = 196.25 \]

In this equation:

• \(75h\) represents the hourly charges,
• 65 is the visit fee,
• and \(196.25\) is the total cost \(Xavien\) paid.

Thank you for clarifying your request!