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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?

You can travel 840 miles from the broken supply truck. Since your base camp is 800 miles away (half of 1600 miles), you can easily complete the delivery. Here's how:

Although you can only carry one barrel at a time, you need to transport both of them until one barrel is empty. F is the barrel used first, and L is the barrel used last.

Use half of a tank (5 gallons) to carry L 5*12=60 miles, and then return for F (uses another 5 gallons). Refill the tank from F and carry it to where you left L (also uses 5 gallons). Refill the tank again from F and switch barrels. Now you are 60 miles from the broken truck, the tank and L are full, but F is down to 30 gallons (45-5-5-5=30). Repeat this procedure two times.

Now you are 60*3=180 miles from the broken truck. The tank and L are still full, but F is empty. Leave F behind and make a run for it, carrying L. Refill the tank from L as needed. There are 55 gallons of fuel left so you can travel an additional 55*12=660 miles, for a maximum of (180+660) 840 miles. Since you only have a total of 800 miles to go, you will make it to your base camp.

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