A Certain Truck Traveling at 55 miles per hour gets 4.5 miles per Gall GMAT Problem Solving

Question: 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?

1. 140
2. 200
3. 250
4. 300
5. 360

Answer:

Approach Solution (1):

4.5 miles/gallon = \(\frac{9}{2}\) miles/gallon at 55 mph

3.5 miles/gallon = \(\frac{7}{2}\) miles/gallon at 60 mph

\(\frac{500}{120}\)= 4.1667 = 4 *\(\frac{1}{6}\)=\(\frac{25}{6}\)miles/gallon average

Note that we are taking the average of miles/gallon. The weights will be gallons, not miles.

 \(\frac{w_1}{w_2}\)= \(\frac{(A_2-A_{avg})}{(A_{avg}-A_1)} = \frac{\frac{7}{2}-\frac{25}{6}}{ \frac{25}{6}-\frac{9}{2}} \)=\(\frac{\frac{-4}{6}}{\frac{-1}{6}} = \frac{2}{1} \)

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

Correct Option: E

Approach Solution (2):

Let the truck used x gallons of fuel traveling at 55 mph, then it used (120 – x) gallons of fuel traveling at 60 mph.
So, in x gallons of fuel traveling at an economy of 4.5 miles per gallon it traveled 4.5x miles, and in (120 – x) gallons of the fuel traveling at an economy of 3.5 miles per gallon it traveled 3.5 (120 – x) miles

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

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

Correct Option: E

“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?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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