John takes 6.5 hours to travel from city A to city B at 3 different

Question

John takes 6.5 hours to travel from city A to city B at 3 different speeds 30 mph, 45 mph, and 60 mph, covering equal distance with each speed. The respective mileages per liter of fuel are 11 miles, 14 miles, and 18 miles for the above speeds. John's friend Adam is an efficient driver and wants to minimise his friend's car's fuel consumption. Therefore, Adam decides to drive Ramesh's car one day from city A to city B. How much fuel will he be able to save?

A. 4.2 liters
B. 4.5 liters
C. 7 liters
D. 2.5 liters
E. 5 litres

Show Answer

Official Answer

B

A. 4.2 liters
B. 4.5 liters
C. 7 liters
D. 2.5 liters
E. 5 litres

effatara · Accepted Answer

Let the distance from A to B be 3d miles. Then:
6.5 hrs = d/30 + d/45 = d/60---> d = 90 miles. Total distance from A to B is 270 miles.
John's fuel consumption = 90/11 + 90/14 + 90/18 = 19.61 liters
In order to minimize fuel consumption, Adam will obviously drive the entire distance at the speed with the maximum miles per liter i.e. 18.
Therefore, Adams fuel consumption is 270/18 = 15 liters
Fuel saved = 19.61 - 15 = 4.61 liters
The closest answer is B.

neelgmat · Answer

Hi
Can you please explain how to calculate the following fast without a calculator:
"90/11 + 90/14 + 90/18 = 19.61 liters"
Thanks in advance

Posted from my mobile device

effatara · Answer

neelgmat , 
Please see attachment.

CrackverbalGMAT · Answer

To start off with, I think the author means John when he says Ramesh in the last statement of this question.

This is a fairly straightforward question on speed , time and distance with a wee bit of minimization principle involved towards the end of the solution.

Since John covers equal distance at the given speeds, let us assume the LCM of 30, 45 and 60 as this distance. The LCM of 30, 45 and 60 is 180. Then, the total time taken to travel from A to B will be

\frac{180}{30}  +  \frac{180}{45}  +  \frac{180}{60}  = 6 + 4 + 3 = 13. { Time =  \frac{Distance}{Speed} }

But the question says that John took 6.5 hours to travel from A to B. Therefore, each segment has to be 90 miles each; so the distance from A to B should be 270 miles.

The question also says that the fuel consumption is 11 miles per liter (mpl) when the speed is 30mph, 14mpl when the speed is 45 mph and 18mpl when the speed is 60 mph. 
Therefore, the fuel consumption is lowest at a higher speed. So, if one has to minimize fuel consumption, he/she has to drive at 60 mph.

Since John drove 90 km each at the three different speeds, the total fuel consumption will be

\frac{90}{11}  +  \frac{90}{14}  +  \frac{90}{18}  = 8.1 + 6.4 + 5 = 19.5 liters.

However, since Adam wants to minimize the fuel consumption, he can do so by driving all the 270 miles at 60mph. If he does this, the total fuel consumed will be

\frac{270}{18}  = 15 litres.

So, he will be able to save 4.5 litres. The correct answer option is B.

Hope this helps!

AnirudhaS · Answer

I did it this way, did not take long. but got to the wrong answer.

90(1/11 + 1/14 + 1/18)
=90(0.09 + 0.07 + 0.05) - approx  
=90(0.21)
=18.9

18.9 - 15 = 3.9, which is closer to 4.1

I am a bit confused, how do we know calculating to what precision is enough. I do get that I am wrong, just to understand how we get on with this type of problems.

effatara · Answer

AnirudhaS

You went for the decimal values too soon. Please go through attachment the attachment again. You will have to work with fractional values right until you get a single fraction which you can convert to decimal value to match with answer options.
Best of luck!

samarpan.g28 · Answer

First, let's calculate distance.
d/(3*30)+d/(3*45)+d/(3*60)=6.5 =>d=270 i.e. distance is divided in three equal parts of 90 miles each.
Now, for every 90 miles, the fuel used is 90/11+90/14+90/18=19.6 l.
To save fuel, travel the entire 270 miles, travel using the speed that gives maximum mileage i.e. 18. So, 270/18=15l. Thus, 19.4-15=4.6l is saved (B).

John takes 6.5 hours to travel from city A to city B at 3 different

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

John takes 6.5 hours to travel from city A to city B at 3 different

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards