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

neelgmat,
Please see attachment.

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!

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 [now i stopped calculating after 2 decimals]
=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.

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!

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).