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A car traveled 462 miles per tankful of gasoline on the hig
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05 Feb 2020, 07:45
05 Feb 2020, 07:45
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Question Stats:
56% (02:36) correct
43% (02:32) wrong based on 179 sessions
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A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
(A) 14
(B) 16
(C) 21
(D) 22
(E) 27
(A) 14
(B) 16
(C) 21
(D) 22
(E) 27
Re: A car traveled 462 miles per tankful of gasoline on the hig
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05 Feb 2020, 08:18
05 Feb 2020, 08:18
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Asif123 wrote:
A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
(A) 14 (B) 16 (C) 21 (D) 22 (E) 27
(A) 14 (B) 16 (C) 21 (D) 22 (E) 27
Same tankful resulted in car driving 462 – 336 = 126 miles more on the highway compared to the city.
It is also stated that on the highway the car traveled 6 more miles per gallon. From this we can calculate the tankful as 126 miles / (6 miles/gallons) = 21 gallons.
Number of miles in the city using tankful is 336/21 = 16
P.S.: To double check: the number of miles on highway using tankful is 462/21 = 22 which is 6 more.
Re: A car traveled 462 miles per tankful of gasoline on the hig
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01 Sep 2020, 15:39
01 Sep 2020, 15:39
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Asif123 wrote:
A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
(A) 14
(B) 16
(C) 21
(D) 22
(E) 27
(A) 14
(B) 16
(C) 21
(D) 22
(E) 27
So we're looking for:
\(\frac{miles}{gallon}\)
and we're given:
\(\frac{miles}{tank}\), where the tank consists of a fixed maximum number of gallons.
To find out the number of gallons in the tank, we can think of it as a ratio:
\(\frac{gallons}{tank}\)
Writing this out, we get:
\(\frac{462 miles}{tank}\) on the highway.
\(\frac{336 miles}{tank}\) in the city.
We also know that the car in the city drove 6 miles less than the car did on the highway. Let \(x\) be the number of miles driven on the highway. It follows that \(x-6\) miles we're driven in the city. This can be written as:
\(\frac{(x)miles}{gallons}\) on the highway.
\(\frac{(x-6)miles}{gallons}\) in the city.
To find the gallons per tank we can simply divide miles/tank by miles/gallons to eliminate the miles:
\(\frac{462 miles}{tank} / \frac{(x) miles}{gallons}\)
\(\frac{336 miles}{tank} / \frac{(x-6) miles}{gallons}\)
This simplifies to:
\((\frac{462 miles}{tank}) * (\frac{gallons}{(x) miles})\)
\(\frac{462 miles}{(x) miles}\) \(\frac{gallons}{tank}\)
And:
\(\frac{336 miles}{tank} * \frac{gallons}{(x-6) miles}\)
\(\frac{336 miles}{(x-6) miles}\) \(\frac{gallons}{tank}\)
The miles cancel and we're left with:
\(\frac{462}{x}\) \(\frac{gallons}{tank}\)
\(\frac{336}{(x-6)}\) \(\frac{gallons}{tank}\)
Now we can simply equal them to eachother to solve for \(x\):
\(\frac{462}{x}\) \(=\) \(\frac{336}{(x-6)}\)
\(462x - 2772 = 336x\)
\(-2772 = -126x\)
\(x = 22\)
Since we're looking for the number of miles per gallon incurred in the city, we would plug this into the miles per gallon equation written above for the city:
\(\frac{(x-6)miles}{gallon}\) in the city.
\(\frac{(22-6)miles}{gallon}\) in the city.
\(\frac{16miles}{gallon}\) in the city.
So the answer is B
