Two Plumbing companies charge different rates for their service. Clyde's plumbing company
charges a $75 per visit fee that includes one hour of labor plus $45 per hour after the first
hour. We-Unclog-It Plumbers charges $100 per visit fee that includes one hour of labor plus
$40 per hour after the first hour. For how many hours of plumbing work would Clyde's be
less expensive than We-Unclog-It? Justify your answer mathematically.

To determine for how many hours of plumbing work Clyde's Plumbing Company would be less expensive than We-Unclog-It Plumbers, we need to compare the total costs of the two companies.

Clyde's Plumbing Company charges a $75 per visit fee that includes one hour of labor, plus $45 per hour after the first hour.

We-Unclog-It Plumbers charges a $100 per visit fee that includes one hour of labor, plus $40 per hour after the first hour.

Let's call the total number of hours of plumbing work "x".

For Clyde's Plumbing Company, the total cost would be:

$75 + $45(x-1) = $75 + $45x - $45 = $30 + $45x

For We-Unclog-It Plumbers, the total cost would be:

$100 + $40(x-1) = $100 + $40x - $40 = $60 + $40x

To find the number of hours where Clyde's is less expensive, we set the two expressions equal to each other:

$30 + $45x = $60 + $40x

$15 = $5x

x = 3

Therefore, for 3 hours of plumbing work or less, Clyde's Plumbing Company would be less expensive