A truck traveled 336 miles per full tank of diesel on the national hig

The truck travelled 336 miles on national highway while only 224 miles on state highway on the full tank. This is a difference of 336 - 224 = 112 miles.
Per gallon, the truck travelled 4 fewer miles. So if it travelled 112 fewer miles, it means it had 112/4 = 28 gallons of fuel in it.

So miles per gallon on state highway = 224/28 = 8 miles/gallon
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Highway mileage = x + 4

224/x = y
336/(x+4) = y
224/x = 336/(x+4)

896 + 224x = 336x
112x = 896
X = 8 answer choice B

We can also do it by backsolving.

Pick x = 8

224/8 = 28

Now 28 * 12 = 336

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[quote="Salsanousi"]Highway mileage = x + 4

224/x = y
336/(x+4) = y
224/x = 336/(x+4)

896 + 224x = 336x
112x = 896
X = 8 answer choice B

We can also do it by backsolving.

Pick x = 8

224/8 = 28

Now 28 * 12 = 336

Why are in first solution we putting them both equal to each other ?

Miles/ miles per gallon = gallon capacity (full tank)

If I find the capacity of the full tank and multiply it by by the miles/per gallon I get the total mileage per fill tank.

Since we are talking about the same truck then the gallon capacity must be the same.

I hope this is clear

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national highway = x gallon per mile / total distance traveled 336

state highway = x-4 gallon per mile / total distance traveled 224


\(\frac{336}{x} = \frac{224}{x-4}\) cross multiply

\(336(x-4) = 224x\)

\(336x-1344 = 224x\)

\(336x-224x = 1344\)

\(112x=1344\)

\(x =12\)

hence \(12-4 = 8\)

\(\frac{336}{x} = \frac{224}{(x - 4)}\)

Now, use the options -

(A) 336/6 ≠ 224/2 => 56 ≠ 112
(B) 336/8 = 224/4 => 56 = 56, No need to go further Answer must be (B)
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Hi Karishma, can you please help me understand why you use 224/28 to get 8 miles/gallon, please? Since 28 gallons is the amount of fuel the track left in the tank. Thank you in advance!

Let x = the number of miles per gallon the truck traveled on the state highway, we can create the proportion:

336/(x + 4) = 224/x

336x = 224x + 896

112x = 896

x = 8

Answer: B
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On the National the truck gets 336 miles per 1 full tank

On the State the truck gets 224 miles per 1 full tank.

The miles the truck can get on a full tank Decreases by: (224 - 336) / 336 = 112/336 = 1/3

If the truck can get X miles/gallon on the National, then the truck gets (X - 4) miles/gallon on the State.

Since the miles per 1 tank fuel efficiency Decreased by 1/3rd , the miles per gallon fuel efficiency will similarly Decrease by 1/3rd.

Therefore, the miles per gallon the truck gets on State = X - 1/3*X

X - 4 gallons = X - 1/3*X

4 = 1/3*X

X = 12 miles per gallon the truck gets on the National Highway

Since the truck gets 4 fewer miles on the State Highway, the answer is 8 miles per gallon.

B

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