For a 30-mile trip, the fuel consumption of a certain car was 15 miles

Question

For a 30-mile trip, the fuel consumption of a certain car was 15 miles per gallon for the first 10 miles and 45 miles per gallon for the rest of the trip. What was the car's fuel consumption for the trip, in miles per gallon?

A. 25
B. 27
C. 30
D. 33
E. 35

A. 25
B. 27
C. 30
D. 33
E. 35

gmatophobia · Accepted Answer

Amount of fuel used for the first 10 miles =  \frac{10}{15}

Amount of fuel used for the next 20 miles =  \frac{20}{45}

Total Amount of fuel used =  \frac{10}{15} + \frac{20}{45} = \frac{50}{45}

The car's fuel consumption for the trip, in miles per gallon =  \frac{	ext{Distance Travelled}}{ 	ext{Fuel Consumed}}

The car's fuel consumption for the trip, in miles per gallon =  \frac{30}{\frac{50}{45}} = 27

Option B

JatinV2 · Answer

I thought the same
Response via Chat GPT
- It's a great intuition to think about using a weighted average, but there's a subtle reason why it doesn't work directly in this context. The key issue lies in the fact that fuel efficiency is a rate (miles per gallon), and when calculating an overall rate, the correct approach requires taking into account the actual fuel consumed, not just the distances.

### Why Weighted Average Doesn't Work Here

Let's break it down:

1. **Fuel Efficiency as a Rate**:
 - Fuel efficiency (miles per gallon) is a rate, not a direct quantity.
 - To combine rates (like 15 mpg and 45 mpg), you need to consider the actual amount of fuel used, not just the distances.

2. **What Weighted Average Assumes**:
 - A weighted average assumes that you're combining like quantities (e.g., distances, times, etc.) in a way that directly correlates.
 - If you were averaging the distances themselves, you could use a weighted average.

3. **The Correct Calculation**:
 - The correct way to combine different fuel efficiencies is to calculate the total fuel used and then divide the total distance by this total fuel, as we did earlier.

### Example of Misleading Weighted Average

If you incorrectly tried to use a weighted average:

- First part of the trip: 15 mpg for 10 miles.

This gives 35 mpg, which is incorrect because this calculation assumes that the fuel efficiencies can be directly averaged, ignoring the different amounts of fuel used at different efficiencies.

Conclusion
The proper method requires considering the total fuel consumed, not just the distances driven, because fuel efficiency is not a linear function that can be averaged by simple weighted average when mixing different rates. This is why we calculate the total fuel used and then compute the overall efficiency, resulting in 27 mpg instead of 35 mpg.

Kinshook · Answer

delphsan

Given: For a 30-mile trip, the fuel consumption of a certain car was 15 miles per gallon for the first 10 miles and 45 miles per gallon for the rest of the trip.
Asked: What was the car's fuel consumption for the trip, in miles per gallon?

Total fuel consumption in gallons = 10/15 + (30-10)/45 = 2/3 + 4/9 = 10/9 gallons
The car's fuel consumption for the trip, in miles per gallon = 30/(10/9) = 27 miles/ gallons

IMO B

Ankit_Raturi · Answer

Can anybody tell why we cannot solve this question through the weighted average method?

10/30*(15) +20/30*(45) =35

Kavicogsci · Answer

Bunuel   KarishmaB  can u pls explain in depth conceptually why weighted avgs doesnt work here

SimantaSourav · Answer

Why can’t we apply weighted average directly?

Price (works):  Price is ₹/kg; we multiply kg × ₹/kg = ₹, the kg cancels, total cost is obtained, so weighted average works.
 Mileage / fuel efficiency (does not work):  Mileage is miles/gallon; we multiply miles × miles/gallon = miles2/gallon, miles do not cancel, so weighted average does not work.
 Speed (does not work):  Speed is km/hour; we multiply km × km/hour = km2/hour, km does not cancel, so weighted average does not work.
 Work / efficiency (does not work):  Efficiency is work/hour; we multiply work × work/hour = work2/hour, work does not cancel, so weighted average does not work.

GaganB · Answer

The requirement of the question is car's fuel consumption for the trip  "in miles per gallon" . In your approach, 30 (miles) being in the denominator - it wont give us miles per gallon. Rather, gallon per miles.

Further, as per your approach, the multiplication of things is fundamentally wrong --> 10*15/30 -- doesn't make any sense of multiplying miles travelled (10) with miles per gallon (15). Same goes for the second part.

Here is the step by step approach - 
(1) We are given that the fuel consumption is 15 miles per gallon for first 10 miles, and 45 miles per gallon for the remaining 30 miles, i.e.
 
 For first 10 miles, 
 
 15 miles --- 1 gallon  
 
 1 mile --- 1/15 gallon 
 10 miles --- 10/15 gallon   
 
 Similarly for next 20 miles,
 
 45 miles --- 1 gallon 
 1 mile --- 1/45 gallon 
 20 miles --- 20/45 gallon

(2) Now, just like the formula for average speed, we can calculate  miles per gallon  here i.e. Total miles/ total gallon consumed
 
 Miles per gallon = 30 miles/ (10/15) + (20/45) gallon 
 30 * 45 / 50 =   27 miles per gallon

Hope this helps!

For a 30-mile trip, the fuel consumption of a certain car was 15 miles

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For a 30-mile trip, the fuel consumption of a certain car was 15 miles

Prep Toolkit

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