Plowing a field

Let $t$ be the number of days required by Jones and Smith working together to plow the field. In 1 day, Jones can plow $\dfrac{1}{6}$ and Smith $\dfrac{1}{9}$ of the field. Hence, the fractional part of the field which can be plowed in $t$ days by Jones is $\dfrac{t}{6}$ and by Smith is $\dfrac{t}{9}$ . Since the whole field is plowed in $t$ days, the sum of the fractional parts plowed by the men in $t$ days is 1:

$\dfrac{t}{6}+\dfrac{t}{9} = 1$

$9t + 6t = 54$

$t=3.6~\text{days}$