Question

A boat has a 10 gallon gasoline tank and travels at 20mi/hr with a fuel consumption of 16mi/gal when operated at full throttle in still water. The boat is moving upstream into a 5mi/hr current. How far upstream can the boat travel and return on 10 gallons of gasolineif it is operated at full throttle during the entire trip?

Answer 1

consumption rate against current = (15 mile/hour)/(16 miles/gallon)
= 15 gallons/16 hours
= (15/16) gallons/hour

consumption rate with the current = (25 miles/hour)/(16 miles/gallon)
= (25/16) gallons/hour

let t1 hours be the time going against the current
distance = 15t1
let t2 hours be the time going with the current
distance = 25t2
but the went the same distance, so
15t1 = 25t2
t1 = (25/15)t2 = 5t2/3

Time x consumption rate = consumption

t1hrs(15/16) gallons/hrs + t2hrs(25/16)gallons/hr = 10 gallons
t1(15/16) + t2(25/16) = 10
times 16
15t1 + 25t2 = 160
but 15t1 = 25t2
50t2 = 160
t2 = 3.2 hrs = 3 hrs, 12 minutes
t1 = 5.3333 hrs. = 5 hrs. 20 minutes

distance = 25t2 = 80 miles

check: 15(5.33333333...) = 80 miles

So the boat can go 80 miles upstream and come back the same 80 miles.

(Wow, did I just prove that to go 160 miles at a rate of 16 miles/gall would take 10 gallons???)