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

[Natasha1]

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)

 

[PeroK]

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?

 

[Orodruin]

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?

 

[Natasha1]

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

 

[PeroK]

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".