Winston can mow his dads grass in 1 hour less than his brother Will. If they take 2 hours to mow it together then how long would it take Winston alone?

Jan 26, 2016

It takes Winston $\frac{1}{2}$ hour to mow the grass alone.

Explanation:

Let ${T}_{\text{Win}}$ be the time it takes Winston to mow the grass in hours.
Let ${T}_{\text{Will}}$ be the time it takes Will to mow the grass in hours.

Then, from the problem's text, we have

${T}_{\text{Win" = T_"Will}} - 1$

$\implies {T}_{\text{Win" - T_"Will}} = - 1$

and

${T}_{\text{Win" + T_"Will}} = 2$

${T}_{\text{Win" + T_"Will" + T_"Win" - T_"Will}} = 2 + \left(- 1\right)$
$\implies 2 {T}_{\text{Win}} = 1$
$\therefore {T}_{\text{Win}} = \frac{1}{2}$
Thus Winston can mow the grass in $\frac{1}{2}$ hour.