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Difficulty:
75%
(hard)
Question Stats:
54% (02:40) correct
46%
(02:59)
wrong
based on 28
sessions
History
Date
Time
Result
Not Attempted Yet
A Turag airplane flying at a speed of \(300 + x\) miles per hour burns fuel at a rate of \(15 + 10\sqrt{x}\) gallons per minute. If a Turag airplane flies \(3750\) miles at a speed of \(625\) miles per hour, approximately how many gallons of fuel will it burn?
A) 1,200
B) 1,500
C) 65,000
D) 70,000
E) 95,000
A) 1,200
B) 1,500
C) 65,000
D) 70,000
E) 95,000
25 Mar 2026, 16:53
Kudos
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Good problem with a nasty unit trap built in. Let me walk through it.
1. Find x. The speed is 300 + x mph, and we're told the airplane flies at 625 mph. So x = 325.
2. Compute the fuel rate. The rate is 15 + 10*sqrt(x) = 15 + 10*sqrt(325). Now sqrt(325) = sqrt(25 * 13) = 5*sqrt(13). Since sqrt(13) is approximately 3.606, we get sqrt(325) approximately 18.03. So fuel rate is approximately 15 + 180.3 = 195.3 gallons per minute.
3. Find the time. Distance = 3750 miles, speed = 625 mph, so time = 3750/625 = 6 hours. That's 6 * 60 = 360 minutes.
4. Total fuel = 195.3 * 360 approximately 70,308. The answer is D (70,000).
The trap: the fuel rate is in gallons per MINUTE. A lot of people compute 195.3 * 6 = ~1,172 and think "oh that's close to 1,200" and pick A. The test writers put A there for exactly that reason. Any time a rate problem gives you a rate per minute and distances in miles, slow down and convert units before multiplying.
Concept tested here is Functions and Custom Characters combined with unit conversion. The "custom function" wrapper (fuel rate = some expression of x) can look intimidating but just means "plug in the number and evaluate."
1. Find x. The speed is 300 + x mph, and we're told the airplane flies at 625 mph. So x = 325.
2. Compute the fuel rate. The rate is 15 + 10*sqrt(x) = 15 + 10*sqrt(325). Now sqrt(325) = sqrt(25 * 13) = 5*sqrt(13). Since sqrt(13) is approximately 3.606, we get sqrt(325) approximately 18.03. So fuel rate is approximately 15 + 180.3 = 195.3 gallons per minute.
3. Find the time. Distance = 3750 miles, speed = 625 mph, so time = 3750/625 = 6 hours. That's 6 * 60 = 360 minutes.
4. Total fuel = 195.3 * 360 approximately 70,308. The answer is D (70,000).
The trap: the fuel rate is in gallons per MINUTE. A lot of people compute 195.3 * 6 = ~1,172 and think "oh that's close to 1,200" and pick A. The test writers put A there for exactly that reason. Any time a rate problem gives you a rate per minute and distances in miles, slow down and convert units before multiplying.
Concept tested here is Functions and Custom Characters combined with unit conversion. The "custom function" wrapper (fuel rate = some expression of x) can look intimidating but just means "plug in the number and evaluate."
