Question

My three cars can travel the same distance on a tank of gas. My second car gets 6 kilometers per liter more than
my first, but its tank holds 3 fewer liters than my first. My third car gets 6 kilometers per liter less than my first, but its tank holds 6 more liters
than my first. How many kilometers can each car travel on a tank of gas?

Answer 1

Answer:

16

Step-by-step explanation::

wrote on NEML, got it right,

Answer 2

Distance traveled by an car is the ratio of the mileage gives by the car to the total fuel the tank holds. The millage of 6 kilometre per liter in 3 liter the cars can travel 18 kilometre.

Given information

All three cars can travel the same distance on a tank of gas.

The second car gets 6 kilometres per liter more than the first, but its tank holds 3 fewer liters than the first.

The third car gets 6 kilometres per liter less than the first, but its tank holds 6 more liters than the first.

Suppose the first car runs m. kilometre per liter. Then the second car will run (m+6) kilometre per liter and third car runs (m-3) kilometre per liter.

Suppose the first car has l liter in the tank. Then the second car has (l-3) liter and third car has (l+6) liters in her tank.

Distance

Distance traveled by an car is the ratio of the mileage gives by the car to the total fuel the tank holds.

As the distance traveled by the first car is same as the second one. Hence,

$\begin{aligned}\\\dfrac{m}{l} &=\dfrac{m+6}{l-3} \\ml-3m&=ml+6l\\m&=-2l\\\end$

Let the above equation is equation 1.

As the distance traveled by the second car is same as the third one. Hence,

$\begin{aligned}\\\dfrac{m-3}{l+6} &=\dfrac{m+6}{l-3} \\ml-3m+9-3l&=ml+6l+6m+36\\l+m&=-3\\\end$

Put the value of m in the above equation from equation 1,

$l-2l=-3\\l=3$

$m=2\times3=6$

Thus the value of the m is 6.

With the millage of 6 kilometre per liter in 3 liter the cars can travel 18 kilometre.

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