Problem Five: How Far Can You Go?
Nov 8th, 2006 by Allen
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 could make the entire 800 miles. It would entail doubling back for the other drum of fuel a couple of times, but you would still make it to base camp.
Since the net journey is 800 miles, but in order to carry both drums the entire distance one at a time, you must go every mile 3 times. That gives you a total distance traveled of 2400 miles. Since your DPV gets 12 mpg, and you have 2 45 gallon drums, and a full 10 gallon tank, you have (2*45+10)*12=2400.
You should be able to make it just fine.
I think… that (2*45+10)*12 = 1200
- Leave the medical supplies and drive out 180 miles, using 15 gallons of fuel.
- Leave one full drum on the ground.
- Drive back to the truck, using another 15 gallons.
- Load up the medical supplies and drive back to where the other drum is, using another 15 gallons.
- At this point, you’re 180 miles out with a full 10 gallon tank and a full 45 gallon drum, with the medical supplies. Those 55 gallons will get you another 660 miles, and the base camp is only 620 miles away, so that’s more than enough fuel.