MathDB

5

Part of 2008 Chile National Olympiad

Problems(1)

trucker cross the desert if total supply of gasoline at station is 180 ;iters

Source: Chile Finals 2008 L2 p5

10/5/2022
When planning a trip from Temuco to the extreme north of the country, a truck driver notices that to cross the Atacama desert you must cross a distance of 800800 km between two stations consecutive service. Your truck can only store 5050 liters of benzene, and has a yield of 1010 km per liter. The trucker can leave gasoline stored in cans on the side of the road in different points along the way. For example, with an initial total charge of 5050 liters you can travel 100100 km, leave 3030 liters stored at the point you reached, and return to the starting point (with zero load) to refuel. The trucker decides to start the trip and arrives at the first service station with a zero load of fuel.
a) Can the trucker cross the desert if at this service station the total supply is 140140 liters? b) Can the trucker cross the desert if the total supply of gasoline at the station is 180180 liters?
algebracombinatorics