This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Tafuta viwango vya kila mwalimu. Kiwango cha Mr. Kanja ni 1 hati5 dakika. Kiwango cha Miss Kanene ni 1 hati4 dakika. Kiwango cha Mrs. Nyaga ni 1 hati12 dakika. Step 2: Kokotoa kiwango cha jumla wanapofanya kazi pamoja. Ili kupata kiwango cha jumla, tunajumlisha viwango vyao binafsi. Kiwango cha jumla R_jumla = (1)/(5) + (1)/(4) + (1)/(12) hati/dakika. Tafuta Kigawo Kidogo Zaidi cha Pamoja (LCM) cha 5, 4, na 12, ambacho ni 60. R_jumla = (1 × 12)/(5 × 12) + (1 × 15)/(4 × 15) + (1 × 5)/(12 × 5) R_jumla = (12)/(60) + (15)/(60) + (5)/(60) R_jumla = (12 + 15 + 5)/(60) = (32)/(60) Rahisisha kiwango cha jumla: R_jumla = (32 ÷ 4)/(60 ÷ 4) = (8)/(15) hati/dakika Step 3: Kokotoa muda unaohitajika kukamilisha kuweka alama hati 160. Muda = Jumla ya kazi / Kiwango cha jumla Muda = 160 hati ÷ ((8)/(15) hati/dakika) Muda = 160 × (15)/(8) dakika Muda = (160 ÷ 8) × 15 dakika Muda = 20 × 15 dakika Muda = 300 dakika Step 4: Badilisha muda kuwa masaa. 300 dakika = (300)/(60) masaa = 5 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 5 masaa. That's 2 down. 3 left today — send the next one.