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Word problem

On a 1287 long road trip in windy conditions, a family calculates their fuel economy to be 18 miles per gallon over the 2 days it takes to reach their destination. On their 2-day return trip, with a similar wind at their backs, their calculations show a fuel economy of 26 miles per gallon.

2. Calculate the expected fuel economy of their vehicle in ideal (non-windy) conditions (f) as well as the influence of the wind (w) in miles per gallon.


2a. Compare how many gallons of fuel they used for the round trip to the expected usage in ideal (non-windy) travel conditions. Which uses more? By how many gallons? Round to the nearest hundreth, if necessary.
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1 Answer

the average of 18 and 26 is 22 so fuel economy (f) in ideal conditions is 22 miles per gallon.
 
the influence of the wind (w) is 4 miles per gallon
 
with the wind against them, the fuel economy is f - w = 22 - 4 = 18 miles per gallon
 
with the wind behind them, the fuel economy is f + w = 22 + 4 = 26 miles per gallon
 
they traveled 1287 miles each way which is a total 2574 miles.
Using ideal fuel economy 22 miles per gallon, they would use 2574 / 22 = 117 gallons
 
With the wind against them they used 1287 / 18 = 71.5 gallons
With the wind behind them they used 1287 / 26 = 49.5 gallons
Adding the two amounts together they used 71.5 + 49.5 = 121 gallons 
 
Therefore 4 more gallons of fuel were used in windy conditions