Question

Michael finished colouring a picture in $\frac{7}{12}\mathrm{hours}$. Vaibhav finished colouring the same picture in $\frac{3}{4}\mathrm{hours}$. Who worked longer? By what fraction was it longer?

Answer 1

Step 1: Convert the given fractions into like fractions.

From the given data we have,

Time taken by Michael to colour the picture is $\frac{7}{12}\mathrm{hours}$.

Time taken by Vaibhav to colour the picture is $\frac{3}{4}\mathrm{hours}$.

Convert the above fractions into like fractions by taking LCM of the denominators.

The LCM of $12$ and $4$ is $12$.

So, convert the given fractions into like fractions having $12$ as the denominator.

$$\begin{gathered} \frac{7}{12}\times \frac{1}{1}=\frac{7}{12} \\ \frac{3}{4}\times \frac{3}{3}=\frac{9}{12} \end{gathered}$$

Step 2: Compare the two fractions to find out who worked longer and by what fraction.

Clearly, $\frac{7}{12}<\frac{9}{12}$.

So, $\frac{7}{12}<\frac{3}{4}$.

Therefore, Vaibhav worked for longer time.

Let Vaibhav worked longer by $x\mathrm{hours}$.

Therefore,

$\begin{array}{rcl}x& =& \frac{3}{4}-\frac{7}{12}\\ & =& \frac{9}{12}-\frac{7}{12}\\ & =& \frac{9-7}{12}\\ & =& \frac{2}{12}\\ & =& \frac{1}{6}\mathrm{hour}s\end{array}$

Thus, Vaibhav worked longer than Michael by $\frac{\begin{array}{r}1\end{array}}{6}$ hour.