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# A boat has a 10-gallon gasoline tank and travels at 20mph

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A boat has a 10-gallon gasoline tank and travels at 20mph [#permalink]  15 Jul 2003, 04:18
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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 ?
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Brainless

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IMHO: I assume that since the boat runs at 20 mph with a fuel consumption of 16 mpg when operated at full throttle in still water, upstream and downstream the boat will run NOT ONLY at a different speed BUT ALSO with a different fuel consumption.

Let X be a way upstream; thus, a full trip is 2X.

Distance = average Rate of fuel consumption*gallons
2X=Rav*10

Rav should be proportional to the average speed for the round trip.

Sav = 2*15*25/25+15=2*15*25/40=75/4 mph (the average speed for the round trip)

20 mph corresponds to 16 mpg; thus, 75/4 mph should correspond to Rav

Rav=16*75/4*20=15 mpg (the average rate of fuel consumption for the entire trip)

So, 2X=15*10=150, and X=150/2=75 miles
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stolyar wrote:
IMHO: I assume that since the boat runs at 20 mph with a fuel consumption of 16 mpg when operated at full throttle in still water, upstream and downstream the boat will run NOT ONLY at a different speed BUT ALSO with a different fuel consumption.

Let X be a way upstream; thus, a full trip is 2X.

Distance = average Rate of fuel consumption*gallons
2X=Rav*10

Rav should be proportional to the average speed for the round trip.

Sav = 2*15*25/25+15=2*15*25/40=75/4 mph (the average speed for the round trip)

20 mph corresponds to 16 mpg; thus, 75/4 mph should correspond to Rav

Rav=16*75/4*20=15 mpg (the average rate of fuel consumption for the entire trip)

So, 2X=15*10=150, and X=150/2=75 miles

Thanks .. All the time I was trying to equate the fuel comsumption with the miles travelled on each side ..
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Re: PS : Fuel consumption [#permalink]  15 Jul 2003, 22:13
Brainless wrote:
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 ?

I think Stolyar is correct, but I solved it in a different way.

At 20 miles per hour and 16 miles/gallon, that is equal to 20/16 = 5/4 gallons per hour. This rate of consumption is constant throughout the problem.

At 5/4 gallons per hour, the boat will run for 10/(5/4) = 8 hours.

Hence 15 * T1 = 25 * T2 (distances up and down stream are the same)
and T1 + T2 = 8 (total time is 8 hours).

Solve for either T1 or T2 then plug back in to get D = 75 miles.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Re: PS : Fuel consumption   [#permalink] 15 Jul 2003, 22:13
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