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How Far Can You Go?

Math brain teasers require computations to solve.

 Puzzle ID: #31758 Fun: (2.73) Difficulty: (2.71) Category: Math Submitted By: MarcM1098

Your assignment is to make a delivery from the depot to your base camp, 1600 miles away. The trip begins normally, but unfortunately, halfway to base camp, your supply truck breaks down. You have no way to call for help. Luckily, in addition to medical supplies, the truck is carrying a Desert Patrol Vehicle (DPV) and two barrels of fuel.

The DPV has a full 10 gallon tank, but to make room for the medical supplies, it can only carry one of the 45 gallon barrels at a time. While you can't transfer fuel between barrels, you can refill the tank from the barrels. Assume the DPV can get 12 miles per gallon, regardless of the load it carries.

How far can you go? Is it far enough to deliver the medical supplies and the DPV to your base camp?

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 monkeygrl99 Jul 13, 2006 This wasn't hard, but wasn't easy either!! Yaay! First one! dan1234 Jul 13, 2006 Haha, ahhhhhh... "one at a time." scallio Jul 20, 2006 Very clever indeed. Great teaser! Qrystal Jul 20, 2006 Ah, that was fun. Miscounted at the last moment and thought the med supplies were in trouble, but recounted and realized all was good. (user deleted) Jul 22, 2006 when you "Assume"... (user deleted) Feb 02, 2007 Lol I love the "assume" sentiment. hard problem, at least for me. but its late and I'm tired, which probably didnt help . Good job anyways lilredc5 May 24, 2007 Good teaser. You know you would travel the same total distance but save yourself some time moving barrels around if you: begin and go a full 15 gallons worth of distance, leave your supplies there, go back for the second barrel. When you return with the full barrel you can drop off the empty one and pick up your supplies and travel the remaining 55 gallons worth (70 gallons of distance total = 840 miles) javaguru Jan 02, 2009 The answer was far easier to find than the explanation suggests. 100 gallons of fuel means that there is a 1200 mile range. The final sprint with one barrel and a full tank is 55x12 = 660 miles. Up until that point you have to cover the ground 3 times, so the 1200-660=540 miles you travel before emptying the first barrel will take you 540/3 = 180 miles from the truck. 660+180 = 840. I didn't even bother working out the specific trips to get to 180. nejco13 May 22, 2010 How can you start by filling up the truck with a barrel F, when the tank is already full. In order to do that you would have to somehow get that 10 gallons, that are already in tank, out. So there is no way to save that 10 gallons for the "final sprint". You have to use it at start. So when you use that 10 gallons at start, you can get to 40 miles, where you have both full barrels and medical stuff. So from then on you use one full barrel 3 times in order do cover the distance of 180 miles. So now you are at a distance of 220 miles from broken truck and one full barrel of gas. You can cover a distance of 540 miles with that barrel. So you can get to 760 miles from the broken truck. I cant get further than this? nejco13 May 22, 2010 Ok, I Just figured it out. Haha Nice one. opqpop Sep 10, 2010 @lilredc5 When you travel 15 gallons, you have to travel back 15 gallons. That is impossible if you are leaving a barrel and hence coming back with no barrels. This is a great teaser. Kudos to the author.