On a 1287 mile long road trip in windy conditions, a family calculates their fue
ID: 3113195 • 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-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 necessary.Explanation / Answer
The family’s fuel economy on a 1287 long road trip towards their destination, over 2 days, in windy conditions, is 18 miles per gallon and on the return trip, over 2 days, the fuel economy is 26 miles per gallon. This means that the trip towards the family’s destination is against the wind and that the return trip is with the wind at the back.
17. Let the fuel economy of the family’s vehicle in ideal condition be f miles per gallon and that the influence of the wind be w miles per gallon. In windy conditions, the fuel economy during the trip towards the destination is f-w =18…(1) and during the return trip, the fuel economy is f+w=26…(2).On adding the two equations, we get f-w +f+w = 18 +26 or, 2f = 44 so that f = 44/2 = 22. Then, on substituting this value of f in the 2nd equation, we get 22+w = 26 so that w = 26-22 = 4. Thus, f = 22 and w = 4.
18. The fuel consumption is equal to the distance/(fuel economy). Hence, in ideal (non-windy) conditions, the fuel consumption is 2*1287/22 = 117 gallons. The fuel consumption during the trip towards the destination (against the wind) is 1287/18 = 71.5 gallons and the fuel consumption during the return trip is 1287/26 = 49.5 gallons. Therefore, the total fuel consumption in windy condition is 71.5+49.5 = 121 gallons. Thus, in windy condition, the car uses more fuel, by 121-117 = 4 gallons.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.