Answer:
○ 1 hour 41 minutes or more
Step-by-step explanation:
We can make two equations that represent the total amount each plumber charges.
If [tex]x[/tex] represents the number of hours they work, then:
•Total charged by Plumber A = [tex]35 + 15x[/tex]
• Total charged by Plumber B = [tex]40+12x[/tex]
Now, if Plumber A is more expensive than Plumber B, then:
Total charged by Plumber A > Total charged by Plumber B
∴ [tex]35 + 15x[/tex] > [tex]40+12x[/tex]
Now all we have to do is solve for [tex]x[/tex]:
[tex]35 + 15x[/tex] > [tex]40+12x[/tex]
⇒ [tex]35 + 15x -12x > 40[/tex]
⇒ [tex]35 + 3x > 40[/tex]
⇒ [tex]3x > 5[/tex]
⇒ [tex]x > \bf \frac{5}{3} \space\ \mathrm{h}[/tex]
[tex]\frac{5}{3} \space\ \mathrm h[/tex] is equivalent to [tex]\frac{5}{3} \times 60 \space\ \mathrm {min}[/tex] = 100 minutes, which is the same as 1h 40min.
This means if Plumber A works more than 1h 40min, they become more expensive than Plumber B.
More than 1h 40min is equivalent to '1 hour 41 minutes or more', therefore the first option is correct.
