You recently started the paperwork to purchase your new home, and you were just notified that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifters and Quick Move, to discuss their rates. Heavy Lifting charges an $80 fee plus $35 per hour. Quick Move charges $55 per hour with no additional fees.

Which mover provides a better deal for 2 hours of work? How did you arrive at your answer?

The obvious way is to calculate the two costs using 2 hours, for which we get

HL = 80 + (35x2) = 150
QM = 55 x 2 = 110

so QM is the cheaper.

More generally you can look as this type of problem based on two lines on a graph. If we plot y=80+35 for HL and y=55 for QM then we have two straight lines which cross where x(or time) = 4 hours. If we plot these we see that provided the time is less than 4 hours QM is the cheaper, for 4 hours they are equal cost, and over 4 hours HL is cheaper.

To determine which mover provides a better deal for 2 hours of work, we need to calculate the total cost for each company.

For Heavy Lifters, they charge an $80 fee plus $35 per hour. Since we need their services for 2 hours, the cost per hour is $35. Therefore, the total cost for 2 hours of work is calculated as:

$80 + ($35 * 2) = $80 + $70 = $150

For Quick Move, they charge $55 per hour with no additional fees. So, for 2 hours of work, the total cost would be:

$55 * 2 = $110

Now we can compare the total costs. Heavy Lifters' total cost is $150, while Quick Move's total cost is $110.

Based on the calculations, it is evident that Quick Move provides a better deal for 2 hours of work, as it offers a lower total cost of $110 compared to Heavy Lifters' total cost of $150.