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Find an expression in terms of v in terms of p, b and a

  1. Oct 18, 2014 #1
    1. The problem statement, all variables and given/known data
    If a car has p litres of petrol in the tank it can travel a kilometres. With v litres of petrol in the tank it can travel b kilometres. Find an expression in terms of v in terms of p, b and a.

    2. The attempt at a solution


    I just cross-multiplied how I was shown in class, and get v = (p * b) divided by a

    So my question is first is this answer correct, and if so, how to demonstrate in perhaps a few steps how I get to it. As I do not understand logically why this is the answer (if it is)
     
  2. jcsd
  3. Oct 18, 2014 #2

    PeroK

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    Here's how I'd look at it:

    With p litres it can travel a kilometres. So, with p/a litres it can travel 1 kilometre. Does that make sense?

    Can you now do the next bit?
     
  4. Oct 18, 2014 #3

    Orodruin

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    Yes, it is correct. What part in the derivation are you unsure about? The first question to ask would be: How much fuel is spent per kilometer travelled?
     
  5. Oct 18, 2014 #4
    Ahhh, so with v litres it can travel b kilometres. So, with v/b litres it can travel 1 kilometre.

    So, if 1 litre = 1 litre

    then, v/b = p/a

    So v = (p/a) * b
     
  6. Oct 18, 2014 #5

    PeroK

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    Yes, although I'd actually look at it slightly differently:

    It takes p/a litres to go 1 kilometre.

    So, to go b kilometres it takes b*(p/a) litres. So, v = b*(p/a).

    With all such problems it's often a good idea to think how much to go 1 kilometre. Or, how far can you go on 1 litre.

    You could, in fact, do the problem again thinking "how far can you travel on 1 litre".
     
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