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

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Homework Help Overview

The problem involves a car's fuel consumption, specifically relating the amount of petrol in litres to the distance it can travel in kilometres. The original poster seeks to find an expression for the amount of petrol (v) in terms of the known quantities (p, b, and a).

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss cross-multiplication as a method for deriving the expression and question the logical basis for the resulting formula. There are attempts to understand the relationship between fuel consumption and distance traveled, with some participants suggesting alternative perspectives on the problem.

Discussion Status

Some participants express confidence in the correctness of the derived expression, while others seek clarification on specific steps in the reasoning process. There is an ongoing exploration of different ways to conceptualize the relationship between fuel and distance.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the depth of exploration and the types of solutions discussed. There is an emphasis on understanding the derivation rather than simply arriving at an answer.

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Homework Statement


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)
 
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Natasha1 said:

Homework Statement


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)

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?
 
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?
 
PeroK said:
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?

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
 
Natasha1 said:
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

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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