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

1. Oct 18, 2014

Natasha1

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. Oct 18, 2014

PeroK

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?

3. Oct 18, 2014

Orodruin

Staff Emeritus
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?

4. Oct 18, 2014

Natasha1

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

5. Oct 18, 2014

PeroK

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".