# Problem of the Week

Problem B and Solution

Running Low on Gas

## Problem

Driving home from a meeting late one evening, Ming notices that her gas gauge is showing that a mere \(\frac{1}{10}\) of a tank remains. Luckily, just then she spots a \(24\)-hour gas station. She has just enough money to add \(20\) litres of gas to the tank, bringing her gas tank up to \(\frac{1}{2}\) full.

Given that the gas tank went from \(\frac{1}{10}\) full to \(\frac{1}{2}\) full, determine the fraction of the tank filled by the gas that Ming added. Hint: Use equivalent fractions.

The fraction of the tank you found in part (a) holds \(20\) L. How many litres are there in \(\frac{1}{10}\) of a full tank?

Given what you discovered in part (b), what is the full capacity, in litres, of Ming’s gas tank?

## Solution

Driving home from a meeting late one evening, Ming notices that her gas gauge is showing that a mere \(\frac{1}{10}\) of a tank remains. Luckily, just then she spots a \(24\)-hour gas station. She has just enough money to add \(20\) litres of gas to the tank, bringing her gas tank up to \(\frac{1}{2}\) full.

Given that the gas tank went from \(\frac{1}{10}\) full to \(\frac{1}{2}\) full, determine the fraction of the tank filled by the gas that Ming added. Hint: Use equivalent fractions.

The fraction of the tank you found in part (a) holds \(20\) L. How many litres is there in \(\frac{1}{10}\) of a full tank?

Given what you discovered in part (b), what is the full capacity, in litres, of Ming’s gas tank?

**Solution**

Since \(\frac{1}{2}= \frac{5}{10}\) and Ming started with \(\frac{1}{10}\) of a tank, the gas Ming added filled \[\frac{5}{10}\text{ of a tank}-\frac{1}{10}\text{ of a tank} = \frac{4}{10}\text{ of a tank.}\]

Since \(\frac{4}{10}\) of a tank holds 20 litres, \(\frac{1}{10}\) of a tank holds \(20\div 4=5\) litres.

Since \(\frac{1}{10}\) of a tank holds \(5\) litres, the full capacity of Ming’s tank is \(10\times 5 = 50\) litres.