Bunuel wrote:
A boat has a 10-gallon gasoline tank and travels at 20 miles per hour with a fuel consumption of 16 miles per gallon when operated at full throttle in still water. The boat is moving upstream into a 5 miles per hour current. How far upstream can the boat travel and return on 10 gallons of gasoline if it is operated at full throttle during the entire trip ?
A. 65 miles
B. 70 miles
C. 75 miles
D. 80 miles
E. 85 miles
A boat has a 10-gallon gasoline tank and travels at 20mph with a fuel consumption of 16mi/gallon when operated at full throttle in still water. The boat is moving upstream into a 5mph current. How far upstream can the boat travel and return on 10 gallons of gasoline if it is operated at full throttle during the entire trip ?
At full throttle, boat travels 16 miles per gallon
--> Total distance = 16*10 = 160 miles (for 10 gallons)
--> Total time boat can travel = 160/20 = 8 hours
Let the time taken for upstream = \(t_1\) & for downstream = \(t_2\)
--> \(t_1 + t_2 = 8\)
Speed during upstream = 20 - 5 = 15 mph & during downstream = 20 + 5 = 25 mph
Let the distance traveled in upstream and downstream = d each
--> \(\frac{d}{15} + \frac{d}{25} = 8\)
--> \(\frac{(5d + 3d)}{75} = 8\)
--> \(\frac{8d}{75} = 8\)
--> \(d = 75\) miles
IMO Option C