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

Given: 

Michael finished coloring a picture in  $\frac{7}{12}$ hour.

To do: 

We have to find who worked longer and by what fraction it was longer.

Solution:

Time taken by Michael to colour the picture $=\frac{7}{12}$ hour

Time taken by Vaibhav to colour the picture $=\frac{3}{4}$ hour

Comparing fractions $\frac{7}{12}$ and $\frac{3}{4}$, we get, 

LCM of 12 and 4 is 12

This implies,

$\frac{3}{4}=\frac{3\times3}{4\times3}$

$=\frac{9}{12}$

Here, $\frac{9}{12}>\frac{7}{12}$

This implies,

Vaibhav worked for longer time.

Vaibhav worked for longer time by,

$\frac{9}{12}-\frac{7}{12}=\frac{9-7}{12}$

$=\frac{2}{12}$

$=\frac{1}{6}$

Therefore,

Vaibhav worked longer by a fraction of $\frac{1}{6}$ hour.