My doubt in the following question is that why the average galloons of fuel used is calculated by the formula -
Total distance / Total fuel used instead of Total fuel used/ Total distance travelled?As to what I understand is when we calculate lets say - average age of 5 students, we calculate it by : Total (sum) age / Count
But here in the solution shown it is just the opposite.
Question:
A truck's fuel efficiency varies with its speed. At 60 miles per hour, the truck's fuel efficiency is 18 miles per gallon; at 70 miles per hour, the truck's fuel efficiency is 14 miles per gallon. If the truck travels for 4.5 hours at 60 miles per hour and for 3 hours at 70 miles per hour, what is the average gallons of fuel it uses per mile over the entire journey?
15.5
16
17
30
64
The question presents a truck's fuel use rates at two different speeds and the time the truck spends traveling at those speeds. It will be necessary to determine the total number of miles the truck travels and the total amount of fuel it uses.
State the Task
Determine the average number of gallons of fuel the truck uses per mile over the entire trip.
Approach Strategically
First, note that since the truck's fuel efficiency is 14 mpg for one part of the trip and 18 mpg for the other part of the trip, the average fuel usage must lie between 14 and 18. On this basis, eliminate (D) and (E).
There are a lot of numbers in this question, so organize the information on your noteboard. Begin by using the distance = rate ×time formula to find the total miles traveled.
Distance = Rate x Time
Leg 1 270 60 4.5
Leg 2 210 70 3.0
Total 480
Now find the number of gallons of fuel consumed, using the different rates of usage for each leg of the journey.
270 miles* 1 galloon/18 miles = 15 galloons
210 miles* 1 galloon/14 miles = 15 galloons
The total number of gallons consumed is 30. Finally, find the average miles per gallon by dividing the total miles by total gallons: 480 miles ÷ 30 gallons = 16 mpg, choice (B).
Attachments
File comment: Here is the entire solution. The result is derived by dividing total distance/ total fuel used.

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