A farmer has three oxen. One ox ploughs an acre of land in x hours, the other ox ploughs the same acre of land in y hours and the third ox uses 12 hours to plough the same piece of land. If three oxen are used at the same time, it takes 4 hours to plough the acre of land, find the value of y.

Kiwango cha kazi ni kiasi cha kazi kinachofanywa kwa kila kitengo cha muda. Katika kesi hii, kazi ni kulima ekari 1 ya ardhi.

• Ng'ombe wa kwanza hulima ekari 1 kwa saa 9. Kiwango chake ni $\frac{1}{9}$ ya ekari kwa saa.
• Ng'ombe wa pili hulima ekari 1 kwa saa $y$. Kiwango chake ni $\frac{1}{y}$ ya ekari kwa saa.
• Ng'ombe wa tatu hulima ekari 1 kwa saa 12. Kiwango chake ni $\frac{1}{12}$ ya ekari kwa saa.
• Ng'ombe wote watatu wakifanya kazi pamoja, hulima ekari 1 kwa saa 4. Kiwango chao cha jumla ni $\frac{1}{4}$ ya ekari kwa saa.

Ili kufanya hivyo, toa $\frac{1}{9}$ na $\frac{1}{12}$ kutoka pande zote mbili za mlinganyo.

$$\frac{1}{y} = \frac{1}{4} - \frac{1}{9} - \frac{1}{12}$$

Kisha, rahisiisha mlinganyo.

$$\frac{1}{y} = \frac{9}{36} - \frac{4}{36} - \frac{3}{36}$$ $$\frac{1}{y} = \frac{9 - 4 - 3}{36}$$ $$\frac{1}{y} = \frac{2}{36}$$ $$\frac{1}{y} = \frac{1}{18}$$

Kwa kuwa $\frac{1}{y} = \frac{1}{18}$, basi $y$ lazima iwe 18.

$$y = 18$$

Thamani ya $y$ ni 18 saa.

The value of $y$ is:

$$18$$