Mr. Kanja, Miss Kanene and Mrs Nyaga have to mark a form three math contest for 160 students. They take 5mins, 4mins, and 12mins respectively to mark a script. If they all start to mark at 9.00 am non-stop, what is the shortest time they can take to complete the marking?

Kiwango cha Mr. Kanja ni $\frac{1 \text{ hati}}{5 \text{ dakika}}$.
Kiwango cha Miss Kanene ni $\frac{1 \text{ hati}}{4 \text{ dakika}}$.
Kiwango cha Mrs. Nyaga ni $\frac{1 \text{ hati}}{12 \text{ dakika}}$.

Ili kupata kiwango cha jumla, tunajumlisha viwango vyao binafsi.
Kiwango cha jumla $R_{jumla} = \frac{1}{5} + \frac{1}{4} + \frac{1}{12}$ hati/dakika.
Tafuta Kigawo Kidogo Zaidi cha Pamoja (LCM) cha 5, 4, na 12, ambacho ni 60.

Rahisisha kiwango cha jumla:

Muda = Jumla ya kazi / Kiwango cha jumla
Muda = $160 \text{ hati} \div \left(\frac{8}{15} \text{ hati/dakika}\right)$
Muda = $160 \times \frac{15}{8}$ dakika
Muda = $(160 \div 8) \times 15$ dakika
Muda = $20 \times 15$ dakika
Muda = 300 dakika

$300 \text{ dakika} = \frac{300}{60} \text{ masaa} = 5 \text{ masaa}$.

Muda mfupi zaidi wanaoweza kuchukua kukamilisha kuweka alama ni 5 masaa.
Ikiwa wataanza saa 9:00 asubuhi, watamaliza saa 9:00 asubuhi + 5 masaa = 2:00 mchana.

Muda mfupi zaidi wanaoweza kuchukua kukamilisha kuweka alama ni $\boxed{\text{5 masaa}}$.