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Math Help - Please help me with this question!

  1. #1
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    Please help me with this question!

    You decide to enter the world of business and form your own taxi company to transport customers in the inner city for a maximum distance of 10 km. Your aim is to provide great service while making as much money as possible. You decide on a flagfall of $2 however you are unsure what cost per km to charge customers.

    Trial various cost/km values to determine the cost per km that you should charge to encourage the customers to choose your taxi company instead of the other two taxi companies for most distances.

    Blue taxis - flagfall = $2.50, cost per km = $1.50
    Red taxis - flagfall = $1.25, cost per km = $2.25 per km

    I've already worked out at what distance the cost to the customer would be the same for both companies, if that's needed?

    The question then says Hint: are there any travel distances where one of the other companies might still be chosen by a customer?

    Please help me start off and work through this question - I have no idea where to start!

    Thankyou in advance
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  2. #2
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    Quote Originally Posted by bemypenguinxx View Post
    You decide to enter the world of business and form your own taxi company to transport customers in the inner city for a maximum distance of 10 km. Your aim is to provide great service while making as much money as possible. You decide on a flagfall of $2 however you are unsure what cost per km to charge customers.

    Trial various cost/km values to determine the cost per km that you should charge to encourage the customers to choose your taxi company instead of the other two taxi companies for most distances.

    Blue taxis - flagfall = $2.50, cost per km = $1.50
    Red taxis - flagfall = $1.25, cost per km = $2.25 per km

    I've already worked out at what distance the cost to the customer would be the same for both companies, if that's needed?

    The question then says Hint: are there any travel distances where one of the other companies might still be chosen by a customer?
    You know that at 5km, you will be charged $ 1.67 for both company. Now, what if you were to travel 6km? Which taxi will be cheaper?

    Subsitute y=6 and solve for x (for both red and blue taxi) and see which is better value for money (ie which is cheaper).
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  3. #3
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    Ok thankyou very much I'm working with that now and will post my answer here later. Could you maybe help me check this answer? http://www.mathhelpforum.com/math-he...-best-fit.html

    Thankyou!
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  4. #4
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    Ahh I thought that made sense but I'm still stuck :S What type of equation do I use to substitute y=5 for y=6??? Thanks for your help.
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  5. #5
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    Quote Originally Posted by bemypenguinxx View Post
    Ahh I thought that made sense but I'm still stuck :S What type of equation do I use to substitute y=5 for y=6??? Thanks for your help.
    These are your two equation that you found earlier:

    \textcolor{blue}{\text{Blue}} \rightarrow y=1.5x+2.5
    \textcolor{red}{\text{Red}} \rightarrow y=2.25x+1.25

    We found that for $ 1.67, they both travel 5km.

    But, we want to know which would be better value for money. So, we want to see how much it would cost to travel 6km.

    y is your km travelled so substitute y=6 into both equation once at a time and solve for x.

    You will find that one of the taxi will travel 6km for a lower price which would be your better value for money.
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