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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] New post 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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 [#permalink] New post 15 Jul 2003, 06:09
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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 [#permalink] New post 15 Jul 2003, 14:46
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] New post 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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MBA, Anderson School of Management, UCLA, Class of 1993

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