# Mathematic Puzzle

#### Damb.

##### New member
Hey guys,
so I have been given a puzzle which I am not sure how to solve and i wasn't sure which forum to post it under so I chose this one.
I can't quite figure out the correct model and solution. Any help would be awesome!!

#### Jomo

##### Elite Member
What have you tried? If you show us your work then we have a starting point in guiding you to the solution. In the end we want you to solve your problem with out hints.

#### Damb.

##### New member
Well I have tried assigning variables to the water tank and the fuel tank to try and find an equation but I am struggling to figure out what the correct equation is. I was trying to make equations such as 0.75x = 0.5y and 0x = (5/6)y and I wanted to solve a simultaneous equation to find x but any answer I would get Did not make sense and I feel like I am missing something

#### Jomo

##### Elite Member
Let f = fuel economy and w = weight of the water in the tank. These are said to be proportional. So f=kw for some value k.

After traveling for a distance the water tank is half full and 1/2 a tank of full was consumed. If the water tank was empty the fuel consumed would have been 1/6 of a tank. What kind or relationship can you get from this? Do you need additional variables?

#### Damb.

##### New member
So there has to be a constant value which is the weight of the actual tank not accounting for the water. I’m not sure, I am still a bit confused if I’m being honest

#### Otis

##### Senior Member
So there has to be a constant value which is the weight of the actual tank …
Hi Damb. We're instructed to ignore the fuel tank weight.

#### Damb.

##### New member
I originally assumed that you don’t need to worry about the distance that the truck travels because it remains constant, is this true?

#### Jomo

##### Elite Member
I originally assumed that you don’t need to worry about the distance that the truck travels because it remains constant, is this true?
The distance is changing as the truck moves so I am not sure about the distance being constant. However the distance in the two scenarios are the same.

#### Damb.

##### New member
so I don't know how many litres of fuel the fuel tank can hold and we don't know how man litres of water the tank can hold so using the f=kw we could say that (1/2)y = k 0.75x
(0.75x is the average amount of water over the trip for the first scenario).
But this is what ive been trying to work with the whole time and I feel like it is not the direction you are trying to hint me towards

#### Damb.

##### New member
is it to do with the weight of the fuel tank?

#### Damb.

##### New member
I mean fuel not fuel tank sorry

#### Damb.

##### New member
so weight = litres of water in the tank + litres of fuel in the tank
therefore f = k (litres of water in the tank + litres of fuel in the tank)
therefore when there is no water in the tank the fuel consumption = 1/6 of the fuel in the tank
therefore k must be equal to 1/6
therefore when fuel consumption is half of the tank f = (1/6)*(3/4)*litres of water in the tank + (1/6)*(3/4)*litres of fuel in the tank
then f = (1/8)*(litres of water in the tank + litres of fuel in the tank)
then f - (1/8)*litres of fuel in the tank = (1/8)*litres of water in the tank
as f = (1/2) litres of the tank, then (3/8)* litres of fuel in the tank = (1/8)*litres of water in the tank
therefore 3*litres of fuel in the tank = litres of water in the tank
so tat is obviously wrong but could it be the inverse? 1/3 of the fuel tank will be left?