[boromir9111]

I am given a problem where I have a Jeep with x amount of fuel and I have to pass through the dessert with the distance given later using as little fuel as possible.

I am given the following conditions:

• The jeep always uses the same amount of fuel per distance, independent of it’s load and the road conditions;
• The jeep will not brake down;
• The jeep has one tank. The fuel in the tank is used to drive and to fill the depots;
• There is just one road;
• Depots can be placed anywhere along the road. How that is done is not considered.
• The jeep can take a maximum of 100 litres of fuel.
• The jeep uses one litre of fuel for every 10 km.


I am asked,

"Calculate how many depots you will need and how much fuel is necessary to cross a distance of 2400 km
a) If depots are placed on equal distances of 200km."

one thing is bugging me and i need clarification on. Say, I take 50 litres of fuel to the 200km point and put in 10 litres of fuel into the depot and drive back to the starting point. I repeat this process again, going back to the 200km point with the same amount of fuel.

My question is, will I have done only 200km using 100 litres of fuel or 400km using 100 litres of fuel?

[ghostwalker]

You've driven to the depot, driven back, and then driven to the depot again.

Total distance 3x200=600 km. Fuel used 600/10=60 l, + whatever is left in your tank/depots. IMHO.

[dknt]

(Original post by boromir9111)
x

Clearly you didn't listen to a thing I told you yesterday!

[boromir9111]

(Original post by ghostwalker)
You've driven to the depot, driven back, and then driven to the depot again.

Total distance 3x200=600 km. Fuel used 600/10=60 l, + whatever is left in your tank/depots. IMHO.

ermm...shouldn't it be 400km? and 100 litres? if you're driving back to the starting point and then repeating the process?

[ghostwalker]

(Original post by boromir9111)
ermm...shouldn't it be 400km? and 100 litres? if you're driving back to the starting point and then repeating the process?

Why 400, when you've done 3 trips of 200?

If you add up what you've used, what's still in the tank and what's at the depot, it will come to 100, assuming you put 50 in each time.

[boromir9111]

(Original post by ghostwalker)
Why 400, when you've done 3 trips of 200?

If you add up what you've used, what's still in the tank and what's at the depot, it will come to 100, assuming you put 50 in each time.

I see where you're coming from.

If i was asked the minimum amount of fuel i will need to complete 1100km of journey through the desert and needed to make at least one depot.

Would it go something like this,

take 15 litres of fuel to 50km point, drop in 5 litres into the depot and drive back to the starting point....that's a total of 100km now

Put in 100 litres and drive to the 1000km point and pick up the 5 litres from the depot...so, that would be 115 litres of fuel used?

[ghostwalker]

(Original post by boromir9111)
I see where you're coming from.

If i was asked the minimum amount of fuel i will need to complete 1100km of journey through the desert and needed to make at least one depot.

Would it go something like this,

take 15 litres of fuel to 50km point, drop in 5 litres into the depot and drive back to the starting point....that's a total of 100km now

Put in 100 litres and drive to the 1000km point and pick up the 5 litres from the depot...so, that would be 115 litres of fuel used?

Those figures don't make sense. You'd have travelled 1100+2x50 km. So that's at least 120 litres.

[boromir9111]

(Original post by ghostwalker)
Those figures don't make sense. You'd have travelled 1100+2x50 km. So that's at least 120 litres.

I am using 5 litres to get to the 50km point, drop in 5 litres into the depot and use 5 litres to drive back....tank is 0 now, so top up to 100 litres and complete the remaining 1000km and pick up the 5 litres dropped off from the 50km point. So, 50km there and back and then 1000km comes to 1100. Where am i going wrong?

[ghostwalker]

(Original post by boromir9111)
I am using 5 litres to get to the 50km point, drop in 5 litres into the depot and use 5 litres to drive back....tank is 0 now, so top up to 100 litres and complete the remaining 1000km

What remaining 1000km? You're back at the start; you've got 1100km to go still.

When you leave with 100 litres, you'll get to the 50 km depot, you'll have used 5 litres, so you can top up from the depot, which will then be empty. So you have 100litres in the tank and have travelled 50km. You can travel another 1000 km on that tank, and will then be 1050 km from the start, and run out of fuel, and in the middle of nowhere.

[boromir9111]

(Original post by ghostwalker)
What remaining 1000km? You're back at the start; you've got 1100km to go still.

When you leave with 100 litres, you'll get to the 50 km depot, you'll have used 5 litres, so you can top up from the depot, which will then be empty. So you have 100litres in the tank and have travelled 50km. You can travel another 1000 km on that tank, and will then be 1050 km from the start, and run out of fuel, and in the middle of nowhere.

I see. But when i asked in the beginning about taking 50 litres of fuel to the 200km point, dropping off 10 litres into the depot and then driving back to the starting point, topping up the tank and going back to the 200 km point and putting in 10 litres of fuel again and then driving back to the start, i thought you assumed this to be 600km? meaning, you're counting the journey back as an extra 200km travelled?

[ghostwalker]

(Original post by boromir9111)
I see. But when i asked in the beginning about taking 50 litres of fuel to the 200km point, dropping off 10 litres into the depot and then driving back to the starting point, topping up the tank and going back to the 200 km point and putting in 10 litres of fuel again and then driving back to the start, i thought you assumed this to be 600km? meaning, you're counting the journey back as an extra 200km travelled?

That's the total distance travelled, which is why you've used 60 litres, but it's not how far you've gotten on your 2400 km traverse of the desert. Of that, you've only covered 200km. So, I don't know where you've got the 400 from.

[boromir9111]

(Original post by ghostwalker)
That's the total distance travelled, which is why you've used 60 litres, but it's not how far you've gotten on your 2400 km traverse of the desert. Of that, you've only covered 200km. So, I don't know where you've got the 400 from.

Indeed. I was inclined to think 200km using 100 litres but distance in total is more than that, of course. Thanks!