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

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Re: A truck traveled 336 miles per full tank of diesel on the national hig [#permalink]
[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 ?
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A truck traveled 336 miles per full tank of diesel on the national hig [#permalink]
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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Re: A truck traveled 336 miles per full tank of diesel on the national hig [#permalink]
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Bunuel wrote:
A truck traveled 336 miles per full tank of diesel on the national highway and 224 miles per full tank of diesel on the state highway. If the truck traveled 4 fewer miles per gallon on the state highway than on the national highway, how many miles per gallon did the truck travel on the state highway?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 15

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 $$12-4 = 8$$
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Re: A truck traveled 336 miles per full tank of diesel on the national hig [#permalink]
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Bunuel wrote:
A truck traveled 336 miles per full tank of diesel on the national highway and 224 miles per full tank of diesel on the state highway. If the truck traveled 4 fewer miles per gallon on the state highway than on the national highway, how many miles per gallon did the truck travel on the state highway?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 15

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

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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Re: A truck traveled 336 miles per full tank of diesel on the national hig [#permalink]
Bunuel wrote:
A truck traveled 336 miles per full tank of diesel on the national highway and 224 miles per full tank of diesel on the state highway. If the truck traveled 4 fewer miles per gallon on the state highway than on the national highway, how many miles per gallon did the truck travel on the state highway?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 15

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

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!
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Re: A truck traveled 336 miles per full tank of diesel on the national hig [#permalink]
1
Kudos
Bunuel wrote:
A truck traveled 336 miles per full tank of diesel on the national highway and 224 miles per full tank of diesel on the state highway. If the truck traveled 4 fewer miles per gallon on the state highway than on the national highway, how many miles per gallon did the truck travel on the state highway?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 15

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

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Re: A truck traveled 336 miles per full tank of diesel on the national hig [#permalink]
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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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Re: A truck traveled 336 miles per full tank of diesel on the national hig [#permalink]
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Re: A truck traveled 336 miles per full tank of diesel on the national hig [#permalink]
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