On a 1287 mile long road trip in windy conditions, a family calculates their fue
ID: 3112321 • Letter: O
Question
On a 1287 mile 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-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. 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. 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 hundredth, if necessaryExplanation / Answer
17. Let the fuel economy of the vehicle in ideal(non-windy) condition be f miles per gallon and let the influence of the wind be w miles per gallon. Then f –w = 18…(1) and f+w = 26 …(2).On adding the two equations, we get f-w+f+w = 18+26 or, 2f = 44 so that f = 22. Then, on substituting this value of f in the 2nd equation, we get 22+w = 26 so that w = 26-22 = 4. Thus, , the fuel economy (f) of the vehicle in ideal(non-windy) condition is 22 miles per gallon and the influence of the wind is 4 miles per gallon.
18. The one way road trip is 1287 miles long so that the round trip is 2 *1287 = 2574 miles long. Since the fuel economy (f) of the vehicle in ideal(non-windy) condition is 22 miles per gallon, the vehicle will use fuel to the extent of 2574/22 = 117 gallons for the round trip in ideal(non-windy) condition. In windy condition, the trip towards the destinatin ( against the wind), the fuel consumed will be 1287/18 = 71.5 gallons and the fuel consumed during the return journey ( with the wind)will be 1287/26 = 49.5 gallons. Thus, the total fuel consumed in such conditions,in the round trip, will be 71.5+49.5 = 121 gallons. Hence, in windy condition, the vehicle will use more fuel by 121-117 = 4 gallons.
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