Gmat Prep (is this weighted average?)

My approach-

In city, the trip uses 10/25 Gallons (as 25miles consumes 1 Gallon, 10 miles would consume 10/25)
On the highway, the trip uses 50/40 Gallons (as 40miles consumes 1 Gallon, 50 miles would consume 50/40)

So that gives us-
Total gas consumed = 10/25 + 50/40
=> 33/20 Gallons

Total miles covered in the trip = 10 (in the city) + 50 (on the highway)
= > 60 miles

So, to calculate the avg.,
33/20 gallons consumed for 60 miles
1 gallon consumed for => 60/(33/20)
=> 36.3
~ 36

it seems like a weighted average problem.

The two averages (balancing points) are 25 and 40.

Drove in the city = 10 miles
Drove in the highway = 50 miles

it drove more miles on highway so the average will be more tilted (weighted) towards 50. But how much ?

The answer to how much can be found with ratios - it drove (50/60) or 5/6 of the range of speed between 25 and 40 ..

therefore. 5/6 (40-25) => 5/6 (15) => 5 * (2.5) = 12.5

the average will be tilted 12.5 more towards 40 miles.

Therefore, 25 + 12.5 = 37.5 - rounding off >> 38

(E) - let me know the OA

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