A plane can travel 200 miles on 50 gallons of jet fuel when it flies

Question

A plane can travel 200 miles on 50 gallons of jet fuel when it flies at 10,000 feet. It can travel 300 miles on 50 gallons of jet fuel when it flies at 20,000 feet. Which of the following is closest to the number of miles per gallon that the plane will average if it flies for 1,000 miles at 10,000 feet and 3,000 miles at 20,000 feet?
A. 3
B. 4
C. 5
D. 6
E. 7

A. 3
B. 4
C. 5
D. 6
E. 7

I am slightly confused here. This is the approach I followed. But I got the answer wrong. Can someone help me here:

-> at 10000 feet, mileage is 4 miles/ gallon
-> at 20000 feet, mileage is 6 miles/ gallon

->now it is covering 1000 miles at 10000 feet and 3000 miles at 20000 feet

-> that means that 1/4 = 0.25 distance is covered at 10000 feet and 0.75 distance is covered at 20000 feet

so shouldn't it be :
0.25 * 4 + 0.75*6
=5.5

They are getting 5.33

Pramod1246 · Answer

Plane travels at 
1) 200m using 50g at 10,000ft 
 200/50 = 4m/g at 10,000ft
2) 300m using 50g at 20,000ft 
 300/50 = 6m/g at 20,000ft

Now plane travels at 1000m at 10,000ft 
3) At 10,000ft the plane uses 4m/g to travel 1000m which means it uses 
1000/4 = 250g 
4) At 20,000ft the plane uses 6m/g to travel 3000m which means 
3000/6 = 500g
Now average m/g = (total miles)/ (total gallons used) = (1000+3000)/(250+500) = 5.33m/g which is approximately 5m/g

Posted from my mobile device

minustark · Answer

A plane can travel 200 miles on 50 gallons of jet fuel when it flies at 10,000 feet. It can travel 300 miles on 50 gallons of jet fuel when it flies at 20,000 feet. Which of the following is closest to the number of miles per gallon that the plane will average if it flies for 1,000 miles at 10,000 feet and 3,000 miles at 20,000 feet?
A. 3
B. 4
C. 5
D. 6
E. 7

A. 3
B. 4
C. 5
D. 6
E. 7

I am slightly confused here. This is the approach I followed. But I got the answer wrong. Can someone help me here:

-> at 10000 feet, mileage is 4 miles/ gallon
-> at 20000 feet, mileage is 6 miles/ gallon

Hi,
I think you are right to your calculation. I did the next steps like this:
For 1000 miles, fuels needed at 4 miles/ gallon = 250 gallons.
For 3000 miles, fuels needed at 6 miles/ gallon = 500 gallons
So, average fuels needed = (1000+3000) / (250+500) = 4000/ 750 = 400/ 75 = 5 (25/75) = 5.33, so if we get it rounded, it will be 5 as it is less than 5.5.
 Correct answer is C.

Kinshook · Answer

Given: A plane can travel 200 miles on 50 gallons of jet fuel when it flies at 10,000 feet.It can travel 300 miles on 50 gallons of jet fuel when it flies at 20,000 feet.

Asked: Which of the following is closest to the number of miles per gallon that the plane will average if it flies for 1,000 miles at 10,000 feet and 3,000 miles at 20,000 feet?

At 1000 feet:
miles / gallon = 200/50 = 4 miles/gallon
miles travelled = 1000 miles
Fuel used = 250 gallons

At 20,000 feet:
miles/gallon = 300/50 = 6 miles/gallon
miles travelled = 3000 miles
Fuel used = 500 gallons

Average miles / gallon = Total miles travelled / Total fuel consumed = 4000/750 = 5 1/3 = 5.33 miles/gallon 
which is closest to 5 miles/gallon

IMO C

sujoykrdatta · Answer

At 10000 feet: 
200 miles require 50 gallons
=> 1000 miles require 50/200 x 1000 = 250 gallons

At 20000 feet: 
300 miles require 50 gallons
=> 3000 miles require 50/300 x 3000 = 500 gallons

Thus: 
Total miles travelled = 4000 miles
Total fuel needed = 750 gallons
Efficiency (miles per gallon) = 4000/750 = 16/3 = 5.33 ~ 5

Answer C

lotif · Answer

Hi. Why is it not possible to do

/4000

This would be like a weighted average method. You know for 1000 miles its 4m/g, and 6m/g for 3000 miles, so you're finding the average. You get 5.5m/g so its not quite right but I want to figure out why.

Thanks

Pluck · Answer

I have the same query, why not weighted average.  Bunuel  could you please clarify.

KarishmaB · Answer

We are averaging miles per gallon here. So that means the weights will be "gallons" of fuel used. We cannot "distance" as the weight. Just like when we average speed (miles per hour), the weights must be "time taken" i.e. hours,  not the distance.

Check this blog post:  https://anaprep.com/arithmetic-weights-in-weighted-average/

Hence simply average miles per gallon as Total Miles/Total Gallons = (1000 miles + 3000 miles) /(250 gallons + 500 gallons) = 5.3 miles/gallon

Answer (C)

Usernamevisible · Answer

Step 1: Convert to mpg
10,000 ft → 200/50 = 4 mpg
20,000 ft → 300/50 = 6 mpg

Step 2: Why simple weighted average (alligation) fails

You might think:
weight = miles → (1000, 3000)

Wrong, because mpg is distance per fuel, so the correct weight is fuel consumed, not distance.

Thus the ratio of weights will be

What should be the weights?

We need:

“How many gallons were used at each mpg?”

At 4 mpg → 1000 miles needs 250 gallons
At 6 mpg → 3000 miles needs 500 gallons

Now weights = 250 : 500

A plane can travel 200 miles on 50 gallons of jet fuel when it flies

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A plane can travel 200 miles on 50 gallons of jet fuel when it flies

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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