Fuel for the long drive

A delivery driver planned a journey of four hundred and fifty kilometres each way. Her van uses eight litres of fuel for every hundred kilometres, and its tank holds fifty litres.

A driver planned $450$ km each way. Her van uses $8$ L for every $100$ km, and the tank holds $50$ L.

$d=450\mathrm{km}$, use $\frac{8}{100}L/km$, tank $50\mathrm{L}$.

One way needs eight times four and a half, which is thirty-six litres, so the tank is enough. But there and back is nine hundred kilometres and seventy-two litres, which is more than fifty. She would have to fill up on the way.

One way: $8\times 4.5=36$ L and $36\le 50$, so it is enough. There and back: $2\times 450=900$ km and $8\times 9=72$ L. Since $72>50$, she needs one fill-up.

fill-up $F$: $8\times 4.5=36\le 50$; $8\times 9=72>50\Rightarrow F$.

A full tank alone would take her six hundred and twenty-five kilometres. Experts say never let the tank fall below a fifth, which is ten litres. Then the safe distance is five hundred kilometres.

A full tank: $\frac{50}{8}\times 100=625$ km. Rule: never below a fifth: $50\times \frac{1}{5}=10$ L, so $40$ L can be used, and $\frac{40}{8}\times 100=500$ km.

$\frac{50}{8}\times 100=625$; $50\times \frac{1}{5}=10$; $\frac{40}{8}\times 100=500$.

She stopped at the halfway point. Four hundred and fifty is less than five hundred, so she arrived with plenty to spare, and fourteen litres were still in the tank.

She stopped at the halfway point: $450\le 500$. Fuel left: $50-36=14$ L, and $14\ge 10$.

$450\le 500$; $50-36=14\ge 10$.