A scientific expedition set out to across the Sahara desert from the north to the south, a distance of 1,656 miles. There was no gasoline available along the route that the expedition was to follow. It was, therefore, necessary to store the gasoline at various points along this route, so that the expedition could be made without outside help. A special truck was used that could carry the necessary scientific equipment, as well as 90 gallons of gasoline, including the gasoline in the tank. If this truck was able to use 1 gallon of gasoline for each 12 miles, at which points [in miles] along the route should deposits of gasoline be stored, so that the minimum amount of gasoline would be used for the expedition? Thanks for help.
You have 90 gallons ....you will be able to make it 90 x 12 = 1080 miles
so at the 1080 mile point you will need to have a gasoline cache stored to get you the rest of the way
1656-1080 = 576 more miles which equates to 576miles/12 m/g = 48 gallon stash waiting for you there.
The special truck is allowed to return to the starting point "A" and reload with another 90 gallons of gasoline and proceed along the same route. How many trips to station "A" should it make in order to enable the expedition to complete the journey, using the minimum amount of gasoline?
Here is my take on it:
Suppose the truck starts out at point A and travels 216 miles to point B using 216/ 12 = 18 gallons of gasoline. At point B, the expedition deposits 54 gallons and returns to point A using up the remaining 18 gallons. This trip is repeated, so that another 54 gallons is deposited at point B. Point B, which is 216 miles from point A, now has deposits of 54+54 = 108 gallons of gasoline. The truck then starts out again from point A fully loaded travels to point B, and picks up the 18 gallons there which was used up to make the trip from point A to point B. Thus, there are 90 gallons now stored at point B. Then, fully loaded with gasoline, the truck proceeds to point C which is 576 miles from point A, but only 360 miles from point B. The truck then used up 360 / 12 = 30 gallons to get to point C. The expedition deposits 30 gallons at point C and returns to point B where the empty tanks of the truck are filled with 90 gallons from the gasoline stored there. Then, the truck proceeds again to point C, using 30 gallons, picks up 30 gallons there, and fills the tank again. At a full capacity of 90 gallons, the truck starts out from point C across the desert and travels the remaining 90×12 = 1080 miles to its destination. Thus, the expedition has used three full tanks of gasoline, or 90×3 = 270 gallons!!.
this question is poorly written and each of you have valid points.
Guest the first number you use is 216 miles.
CPhill and I have no idea where you dug that number up from, (maybe the magic garden) but it doesn't matter.
I have a new take on this question.
It says that the truck can carry all the scientific equipment and 90 gallons of fuel.
It stands to reason that if you are doing a fuel dump then the equipment is not needed so more fuel can be carried.
SO for the fuel dumps my truck can safely carry an aditional 54 gallons of fuel. :)
To get across the desert the truck requires 1656/12 = 138 gallons of fuel.
The experiement laden truck can only carry 90gallons so it needs and additional 48 gallons of fuel.
48 gallons = 48*12 = 576 miles
So if the provisions truck places 48gallons of fuel 576 miles into the desert everything will be hunky dory.
To do this the provisions truck will need 48 gallons of fuel plus what it needs for the 2 way trip.
That is (576+576)/12+48 = 96+48 = 90+54 = 144 gallons.
So all together 144+90=234 gallons of fuel will be needed. That is with just one refuel stop :))