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07 Nov 2023, 08:54
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
65% (02:32) correct
35%
(02:40)
wrong
based on 853
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Solomon's truck gets 24 mpg (miles per gallon) when driven at a speed of 40 mph (miles per hour) with no load. His truck's gas mileage decreases 1 mpg for each 500 pounds of added load and it decreases \(\frac{1}{2}\) mpg for each 10 mph of increased speed over 40 mph. Which of the following is a formula for the gas mileage of Solomon's truck when its speed is S mph (S >= 40) and it has a load of L pounds?
A. \(24 - \frac{L}{500} - \frac{S}{2}\)
B. \(24 - \frac{L}{500}-\frac{S}{20}\)
C. \(26 - \frac{L}{500}-\frac{S}{20}\)
D. \(44 - \frac{L}{500}-\frac{S}{2}\)
E. \(44 - \frac{L}{500}-\frac{S}{20}\)
A. \(24 - \frac{L}{500} - \frac{S}{2}\)
B. \(24 - \frac{L}{500}-\frac{S}{20}\)
C. \(26 - \frac{L}{500}-\frac{S}{20}\)
D. \(44 - \frac{L}{500}-\frac{S}{2}\)
E. \(44 - \frac{L}{500}-\frac{S}{20}\)
07 Nov 2023, 10:27
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ChandlerBong
Let's assume that Solomon's truck had the following speed and weight
- Speed = 50mph
- Weight = 500 pounds
Expected Mileage = \(24 - 1 - \frac{1}{2} = 22.50\)
- We have substracted 1 because the load of the truck is 500 pounds
- We have substracted 1/2 because the truck is moving 10 miles above 40
A. 24 - \(\frac{L}{500}\) - \(\frac{S}{2}\) → \(24 - \frac{500}{500} - \frac{50}{2} = 24 - 1 - 25 = -2\) ⇒ Eliminate
B. 24 - \(\frac{L}{500}\) - \(\frac{S}{20}\) → \(24 - \frac{500}{500} - \frac{50}{20} = 24 - 1 - 2.5 = 20.50\) ⇒ Eliminate
C. 26 - \(\frac{L}{500}\) - \(\frac{S}{20}\) → \(26 - \frac{500}{500} - \frac{50}{20} = 26 - 1 - 2.5 = 22.50\) ⇒ Answer
D. 44 - \(\frac{L}{500}\) - \(\frac{S}{2}\)
E. 44 - \(\frac{L}{500}\) - \(\frac{S}{20}\)
Option C
08 Nov 2023, 08:35
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ChandlerBong
Solution:
- Decrease because of L pounds weight \(= -\frac{L}{500}\)
- Decrease because of S speed \(=-\frac{1}{2}\times \frac{(S-40)}{10}=-\frac{S-40}{20}\)
- Final mileage \(=24-\frac{L}{500}-\frac{S-40}{20}\)
\(⇒24-\frac{L}{500}-\frac{S}{20}+\frac{40}{20}\)
\(⇒24-\frac{L}{500}-\frac{S}{20}+2\)
\(⇒26-\frac{L}{500}-\frac{S}{20}\)
Hence the right answer is Option C
