Maths help...

[Spitfir3]

Hey guys,

Very stuck on this question, been thinking about it for ages and I haven't gotten very far. It's not massively complex or advanced but I can't get my head round it...

Basically: Bloke has 2 options, run a car for £10 a week and £0.03 a mile or hire a car for £0.11 a mile.

Need to find equation of a line for both, plot a graph and then find out at what mileage he hits break even point.

I don't even know where to start

Cheers!

 

[Zefan]

Surely it depends entirely on how quickly the miles are travelled.

As in, how many weeks does he take to cover the amount of miles? Or are we talking within the 1 week hire period?

 

[Vonhelmet]

C is cost.
t is time in weeks.
m is mileage.

Option 1: C = 10t + 0.03m
Option 2: C = 0.11m

Not sure how you'd graph the first, given it has two variables... Unless you know he's only hiring it for a week, in which case set t = 1. In such a case, the break even point will be where the lines on the graph intersect, or you can do it with simultaneous equations as follows, assuming t = 1 as above:

10 + 0.03m = 0.11m
10 = 0.08m
m = 125

If he drives 125 miles in a week, he will be at the break even point. Beyond that, option 1 is best. Up to that point, option 2 is best.

 

[nydryl]

Not totally sure what you're asking but check this. Break even at around 125 miles.

http://www.wolframalpha.com/input/?i=y=10+0.03x,+y=0.11x

Doesn't really matter how many weeks the hire is for, averaging 125 miles per week is what's important.

So after say three weeks the equation is

http://www.wolframalpha.com/input/?i=y=30+0.03x,+y=0.11x

and so the total mileage needed to be done is 375 miles, or an average of 125 miles per week.

 

[skippy2421]

As previously said 125 miles per week break even point, graphs are easy. Ofcourse on the assumption t=1, von seems to have it all there

 

[Spitfir3]

Ah! Looks like I kinda had it right the first time then. Although, strangely I couldn't get my head round the axes but considering I knew the gradients probably would be the £ per mile I should've.. doh Really should do this when i'm not tired.

Thanks a lot guys Much appreciated.

 

[mistercrabb]

You need to know how many weeks the driver will be using the car before you can have an accurate answer, as the 'fixed' portion of option 1 relies upon that.