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A certain car travels 18 miles per gallon of gas on city streets...

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Joined: 11 Oct 2017
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A certain car travels 18 miles per gallon of gas on city streets...  [#permalink]

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Updated on: 26 Oct 2017, 21:25
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45% (medium)

Question Stats:

58% (01:56) correct 42% (01:50) wrong based on 43 sessions

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A certain car travels 18 miles per gallon of gas on city streets and 30 miles per gallon of gas on highway. Damaris drives the car to work during the week and travels on city streets and on the highway. She drives the car on the highway more miles than she drives on city streets. How many miles does Damaris drive to work on the highway?

(1) Damaris drives a total of 26 miles.

(2) The car Damaris drives uses 1 gallon of gas to get to work.

Originally posted by ladyrenee95 on 26 Oct 2017, 21:00.
Last edited by chetan2u on 26 Oct 2017, 21:25, edited 1 time in total.
formatted the Q
Math Expert
Joined: 02 Aug 2009
Posts: 6963
Re: A certain car travels 18 miles per gallon of gas on city streets...  [#permalink]

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26 Oct 2017, 21:34
A certain car travels 18 miles per gallon of gas on city streets and 30 miles per gallon of gas on highway. Damaris drives the car to work during the week and travels on city streets and on the highway. She drives the car on the highway more miles than she drives on city streets. How many miles does Damaris drive to work on the highway?

(1) Damaris drives a total of 26 miles.

(2) The car Damaris drives uses 1 gallon of gas to get to work.

hi
there are TWO averages 18/gallon and 30/gallon

(1) Damaris drives a total of 26 miles.
we cannot say anything
insuff

(2) The car Damaris drives uses 1 gallon of gas to get to work.
again insuff

combined
we can get the ratio of distance traveled on both routes
suff
C

solution
(1) weighted average..
so we can say two averages 18 and 30 .. and final average 26..
so gallons used on route 30/gallon = $$\frac{26-18}{30-18} = \frac{8}{12} = \frac{2}{3}$$
distance traveled = $$30*\frac{2}{3} = 20$$
(2) second method
let x distance be traveled on highway, so 26-x will be traveled on streets..
gallons used =$$1 = \frac{x}{30} + \frac{26-x}{18} ............\frac{90 = 3x+130-5x}{90}........2x=40...x=20$$
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Re: A certain car travels 18 miles per gallon of gas on city streets...  [#permalink]

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09 Nov 2017, 06:38
Another method to reach to the answer using c-

Let the gallons used on the Highway be x. Then as per (b), gallons used on Streets is (1-x).

Distance traveled on the Highway= 30(x).

Distance traveled on the streets= 18(1-x)

We can then build the equation- 18(1-x) + 30x = 26.

x= 2/3.

Distance on highway = 30* (2/3)= 20.
Re: A certain car travels 18 miles per gallon of gas on city streets... &nbs [#permalink] 09 Nov 2017, 06:38
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