Question

At the beginning of the road, a tank truck was traveling full of water in water tank, but it began to leak.You can assume that the fuel consumption of the truck is directly proportional to the weight it carries, and that the water flow(in the leakage) and the speed of the truck are constant for the whole journey. After traveling for miles, the truck leaked half of the water from the water tank and consumed half of fuel tank.
If the water tank was empty the truck would have spent a sixth of the fuel tank, if it travelled the same distance and under the same conditions as above.
Disregarding the fuel tank weight, what fraction of the fuel tank would be spent if there was no leak?

Answer 1

Step-by-step explanation:

Step by step solution has been annexed.

Answer 2

Answer:  fraction of the fuel tank would be spent if there was no leak is   $\frac{11}{18}$

Step-by-step explanation:

• Weight of the water = $w$

• Average Weight = $\frac{w+\frac{w}{2} }{2}$

                                    $=\frac{3w}{4}$

• Oil consumed by water

                         $=\frac{1}{2} -\frac{1}{6}$

                         $=\frac{1}{3}$

• Let, $x$ be the oil consumed if there is no leaking

                 ∴$\frac{\frac{3w}{4} }{w}$$=\frac{\frac{1}{3} }{x}$

                    $x=\frac{4}{9}$

• The total fuel consumed

                $=\frac{4}{9} +\frac{1}{6}$

               $=\frac{8+3}{18}$

               $=\frac{11}{8}$