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A generator contains 60 gallons of fuel and uses 2.5 gallons per hour. A more efficient power generator contains 40 gallons of fuel and uses 1.5 gallond per hour. After how many hours do the generators have the same amount of fuel? Which generator runs longer? Justify your answers

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mathecoach

Answer:

After how many hours do the generators have the same amount of fuel?

60 - 2.5x = 40 - 1.5x --> x = 20 hours

Which generator runs longer?

60/2.5 = 24 hours

40/1.5 = 26 2/3 hours

The more efficient power generator runs 2 2/3 hours longer.

Cetacea

a) After 20 hours the generators have the same amount of fuel.

b) The second generator runs longer.

Given: A generator contains 60 gallons of fuel and uses 2.5 gallons per hour.

So after x hours it has = 60 - 2.5x gallons of fuel.

Given: A more efficient power generator contains 40 gallons of fuel and uses 1.5 gallond per hour.

So after x hours it has = 40 - 1.5x gallons of fuel.

Let after x hours the generators have the same amount of fuel.

So,

[tex]60-2.5x=40-1.5x\\60-40=2.5x-1.5x\\20=x\\[/tex]

So,  after 20 hours the generators have the same amount of fuel.

b) First generator runs = 60/2.5 = 24 hours.

Second generator runs = 40/1.5=26.7 hours.

So the second generator runs longer.

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