math 116
posted by lisa on .
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.