# CAT Practice : Speed Time, Races

When driving Arun knows that he has to go at that speed which will give him maximum mileage to reduce fuel consumption!

## Fuel Consumption

Q.16: Ramesh takes 6.5 hours to go from city A to city B at 3 different speeds 30 kmph, 45 kmph, and 60 kmph covering the same distance with each speed. The respective mileages per liter of fuel are 11 km, 14 km and 18 km for the above speeds. Ramesh's friend Arun is an efficient driver and wants to minimise his friend's car's fuel consumption. So he decides to drive Ramesh's car one day from city A to city B. How much fuel will he be able to save?
1. 4.2 liters
2. 4.5 liters
3. 0.7 liters
4. 0.3 liters

Choice B. 4.5 liters

## Detailed Solution

Total time = 6.5 hrs
Let the total distance be x
Ramesh's speeds = 30, 45, 60 kmph

6.5 = ${{x/3 \over 30} {+} {x/3 \over 45} {+} {x/3 \over 60}}$

6.5 = ${{(2x + 4x/3 + x) \over 180} }$

6.5 = ${{(6x + 4x + 3x) \over 540} }$

or x = 270 km

With each speed distance covered = 270/3 = 90 km
Fuel consumed when driving at 30 = 90/11 = 8.1 l
Fuel consumed when driving at 45 = 90/14 = 6.4 l
Fuel consumed when driving at 60 = 90/18 = 5
Total fuel = 8.1 + 6.4 + 5 = 19.5 liters

When Arun drives the car, he should drive at 60 kmph throughout so that he gets the maximum mileage!
Fuel consumption when driving at 60 for entire journey = 270/18 = 15 liters

Difference = 19.5 – 15 = 4.5

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## More questions from Speed Time, Races

"Life is a race ... if you don't run fast ... you will be like a broken undaa" - Veerusahasra Buddhi