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A certain truck traveling at 55 miles per hour gets 4.5 miles per gall

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A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post 21 Sep 2019, 05:05
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A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60 miles per hour, how many miles did it travel at 55 miles per hour?

A. 140
B. 200
C. 250
D. 300
E. 360


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Re: A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post 13 Oct 2019, 20:35
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gmatt1476 wrote:
A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60 miles per hour, how many miles did it travel at 55 miles per hour?

A. 140
B. 200
C. 250
D. 300
E. 360


PS35502.01



4.5 miles/gallon = 9/2 miles/gallon at 55 mph
3.5 miles/gallon = 7/2 miles/gallon at 60 mph
500/120 = 4.1667 = 4(1/6) = 25/6 miles/gallon average

Note that we are taking the average of miles/gallon. The weights will be gallons, not miles.
Check this post: https://www.veritasprep.com/blog/2014/1 ... -averages/

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (7/2 - 25/6) / (25/6 - 9/2) = (-4/6) / (-1/6) = 2/1

So gallons consumed were in the ratio 2:1 for the two speeds of 55 and 60. Total 120 gallons were consumed so 80 gallons at 55 mph and 40 gallons at 60 mph.
To use 80 gallons, he must have traveled 80*4.5 = 360 miles

Answer (E)
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Re: A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post 21 Sep 2019, 05:21
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let distance covered @ 55mph = x
so mileage would be x/4.5
and @ 60 mph ; 500-x ; mileage 500-x/3.5

solve for

x/4.5+500-x/3.5 = 120
x= 360
IMO E

gmatt1476 wrote:
A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60 miles per hour, how many miles did it travel at 55 miles per hour?

A. 140
B. 200
C. 250
D. 300
E. 360


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A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post Updated on: 13 Oct 2019, 02:08
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gmatt1476 wrote:
A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60 miles per hour, how many miles did it travel at 55 miles per hour?

A. 140
B. 200
C. 250
D. 300
E. 360


PS35502.01


Let the truck travels x miles at 55mph and remaining 500-x miles at 60mph

For 1 mile, at 55mph, number of gallons used = 1/4.5
For x miles, number of gallons used = x/4.5 = 2x/9

For 1 mile, at 60mph, number of gallons used = 1/3.5
For 500-x miles, number of gallons used = (500 - x)/3.5 = 2(500 - x)/7

Given, Total gallons used = 120
--> 2x/9 + (1000 - 2x)/7 = 120
--> (14x + 9000 - 18x)/63 = 120
--> 9000 - 4x = 7560
--> 4x = 1440
--> x = 360

IMO Option E

Originally posted by Dillesh4096 on 21 Sep 2019, 05:24.
Last edited by Dillesh4096 on 13 Oct 2019, 02:08, edited 1 time in total.
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Re: A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post 21 Sep 2019, 05:41
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Let the truck used X gallons of fuel travelling at 55mph, then it used (120-X) gallons of fuel travelling at 60mph.

So, in X gallons of fuel travelling at at an economy of 4.5 miles per gallon it traveled 4.5X miles, and in (120-X) gallons of fuel travelling at an economy of 3.5 miles per gallon it traveled 3.5(120-X) miles.
Since the total Distance traveled is 500 miles, the equation becomes:

4.5X + 3.5(120-X) = 500
Solving for X, it comes to 80.

So, distance traveled at a speed of 55mph = 4.5*80 =>360 miles.

Hence, IMO Option E is the answer.
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A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post Updated on: 14 Oct 2019, 00:30
Hello VeritasKarishma
I hope you are doing well.

Your method has worked so far so well for me but when I try in this question, it seems to not work.
Average miles=500/120= 4.17 milles/ Gallon

Let 55milies case be A and 60 miles be B.

To find the ratio of A and B= (3.5-4.17)/(4.17-4.5)= 2/1
At 55 miles per hour, the trust traveled 333.33 miles.
I am sure I am missing something. please help check.

Originally posted by BoundMan on 11 Oct 2019, 07:43.
Last edited by BoundMan on 14 Oct 2019, 00:30, edited 1 time in total.
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Re: A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post 13 Oct 2019, 00:26
VeritasKarishma please help solve this via weighted average method
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Re: A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post 13 Oct 2019, 21:10
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VeritasKarishma,
Thank you
Learning this method has been the best thing.
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Re: A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post 14 Oct 2019, 04:27
akash7gupta11 wrote:
VeritasKarishma,
Thank you
Learning this method has been the best thing.


I agree. This method has one of the best ROI.
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A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post 04 Nov 2019, 17:17
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VeritasKarishma wrote:
gmatt1476 wrote:
A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60 miles per hour, how many miles did it travel at 55 miles per hour?

A. 140
B. 200
C. 250
D. 300
E. 360


PS35502.01



4.5 miles/gallon = 9/2 miles/gallon at 55 mph
3.5 miles/gallon = 7/2 miles/gallon at 60 mph
500/120 = 4.1667 = 4(1/6) = 25/6 miles/gallon average

Note that we are taking the average of miles/gallon. The weights will be gallons, not miles.
Check this post: https://www.veritasprep.com/blog/2014/1 ... -averages/

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (7/2 - 25/6) / (25/6 - 9/2) = (-4/6) / (-1/6) = 2/1

So gallons consumed were in the ratio 2:1 for the two speeds of 55 and 60. Total 120 gallons were consumed so 80 gallons at 55 mph and 40 gallons at 60 mph.
To use 80 gallons, he must have traveled 80*4.5 = 360 miles

Answer (E)


Alternate Method (Also using Weighted Averages)



Method 2:


If the truck went with 55 miles/hr for the whole journey, then it would have gone 4.5 m/g *120 g/tank = 540 miles/tank -> Speed 2
If the truck went with 60 miles/hr for the whole journey, then it would have gone 3.5 m/g *120 g/tank = 420 miles/tank -> Speed 1

Using the w1/w2 formula (where average = 500 miles/tank; weight = tank)

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (540 - 500)/(500 - 420) = 40/80 = 1/2

So while travelling at 55 mph, 2/3 tank * 120 g/tank = 80 g was consumed.
To use 80 gallons, he must have traveled 80*4.5 = 360 miles

Method 3: Slowest & Too many calculations



Let distance travelled by 55miles/hr speed be X
Then distance travelled by 60miles/hr speed be 500-X
500m/120g = 500m/((Xm/4.5m/g) + (500-X)m/(3.5m/g))
1/120 = 500/(2X/9 + 2(500-X)/7)
(14x + 500*18 -18X)/63 = 120
-4X = 120 * 63
4X = 500*18 - 120*63 = 4 (125*18 - 30*63)
X = 125*18 - 30*63
X = 360
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Re: A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post 01 Jan 2020, 18:33
1
gmatt1476 wrote:
A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60 miles per hour, how many miles did it travel at 55 miles per hour?

A. 140
B. 200
C. 250
D. 300
E. 360


PS35502.01


We can let x = the distance traveled at 55 mph. We can create the equation:

120 = x/4.5 + (500 - x)/3.5

120 = 10x/45 + (5000 - 10x)/35

Multiplying by 315, we have:

37,800 = 70x + 9(5000 - 10x)

37,800 = 70x + 45,000 - 90x

37,800 = 45,000 - 20x

20x = 7200

x = 360

Answer: E
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Re: A certain truck traveling at 55 miles per hour gets 4.5 miles per gall  [#permalink]

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New post 06 Jan 2020, 18:38
gmatt1476 wrote:
A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60 miles per hour, how many miles did it travel at 55 miles per hour?

A. 140
B. 200
C. 250
D. 300
E. 360


PS35502.01


Alternative Method: We can use the answer choice to determine the correct answer.

Let's pick B first:
If the truck traveled 200 miles at 55 mph, then it traveled 300 miles at 60 mph.

That means the truck used 200/4.5 gallons of gas at 55 mph, and 300/3.5 gallons of gas at 60.
When you reduce those fractions, you get 400/9 and 600/7
Adding those together, you get approximately 44+86 = 130 total gallons, which is too much.
This means that the truck drove MORE than 200 miles at 55 mph, so A and B are out

Let's pick D next:
If the truck traveled 300 miles at 55 mph, then it traveled 200 miles at 60 mph.
That means the truck used 300/4.5 gallons of gas at 55 mph, and 200/3.5 gallons of gas at 60.
When you reduce those fractions, you get 600/9 and 400/7
Adding those together, you get approximately 67+57 = 124 total gallons, which is STILL too much.

So E has to be the correct answer!
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Re: A certain truck traveling at 55 miles per hour gets 4.5 miles per gall   [#permalink] 06 Jan 2020, 18:38
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