In a 4 by 400 metres relay race, athletes A, B, C and D took 42.91 seconds, 42.95 seconds, 43.11 and 43.06 seconds respectively to do their race. An average of one second is spent on each button exchange. Calculate the time they started the race if they completed at 8:24:36 p.m.

Question

Asked on August 30, 2026Mathematics

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.

Accepted Answer · 2026-08-30T18:30:25.775Z

Huu hapa ni ufumbuzi wa maswali yako: 4. Katika mbio za kupokezana za mita 4 kwa 400, wanariadha A, B, C na D walitumia sekunde 42.91, sekunde 42.95, sekunde 43.11 na sekunde 43.83 mtawalia kukamilisha mbio zao. Wastani wa sekunde moja hutumika kwa kila mabadilishano ya kijiti. Kokotoa muda walioanza mbio ikiwa walimaliza saa 8:24:36 p.m. Step 1: Kokotoa jumla ya muda wa kukimbia wa wanariadha wote. Jumla ya muda wa kukimbia = 42.91 + 42.95 + 43.11 + 43.83 = 172.80 sekunde Step 2: Kokotoa jumla ya muda uliotumika kwenye mabadilishano ya vijiti. Kuna mabadilishano 3 ya vijiti (kutoka A hadi B, B hadi C, na C hadi D). Kila mabadilishano huchukua sekunde 1. Muda wa mabadilishano = 3 × 1 = 3 sekunde Step 3: Kokotoa jumla ya muda wa mbio. Jumla ya muda wa mbio = Jumla ya muda wa kukimbia + Muda wa mabadilishano Jumla ya muda wa mbio = 172.80 + 3 = 175.80 sekunde Badilisha muda huu kuwa dakika na sekunde: 175.80 sekunde = 2 dakika na 55.80 sekunde Step 4: Kokotoa muda wa kuanza mbio kwa kutoa jumla ya muda wa mbio kutoka muda wa kumaliza. Muda wa kumaliza: 8:24:36 p.m. Muda wa mbio: 2 dakika 55.80 sekunde. Ili kutoa, tunahitaji kukopa kutoka dakika: 8:24:36.00 p.m. 0:02:55.80 Kukopa 1 dakika (60 sekunde) kutoka 24 dakika: 8:23:(36.00 + 60.00) p.m. = 8:23:96.00 p.m. Sasa toa: 8:23:96.00 p.m. 0:02:55.80 Muda wa kuanza = 8:21:40.20 p.m. Muda walioanza mbio ni 8:21:40.20 p.m.. 15. Panua na rahisha: (3x - 2y)^2 - (2y + 3x)^2 Step 1: Tumia fomula ya tofauti ya miraba, A^2 - B^2 = (A - B)(A + B). Hapa, A = (3x - 2y) na B = (2y + 3x). Step 2: Kokotoa (A - B). A - B = (3x - 2y) - (2y + 3x) A - B = 3x - 2y - 2y - 3x A - B = (3x - 3x) + (-2y - 2y) A - B = 0 - 4y = -4y Step 3: Kokotoa (A + B). A + B = (3x - 2y) + (2y + 3x) A + B = 3x - 2y + 2y + 3x A + B = (3x + 3x) + (-2y + 2y) A + B = 6x + 0 = 6x Step 4: Zidisha matokeo ya Step 2 na Step 3. (A - B)(A + B) = (-4y)(6x) = -24xy Kupanua na kurahisisha hutoa -24xy. 3 done, 2 left today. You're making progress.

Accepted Answer · 2026-08-30T18:30:25.775Z

Huu hapa ni ufumbuzi wa maswali yako: 4. Katika mbio za kupokezana za mita 4 kwa 400, wanariadha A, B, C na D walitumia sekunde 42.91, sekunde 42.95, sekunde 43.11 na sekunde 43.83 mtawalia kukamilisha mbio zao. Wastani wa sekunde moja hutumika kwa kila mabadilishano ya kijiti. Kokotoa muda walioanza mbio ikiwa walimaliza saa 8:24:36 p.m. Step 1: Kokotoa jumla ya muda wa kukimbia wa wanariadha wote. Jumla ya muda wa kukimbia = 42.91 + 42.95 + 43.11 + 43.83 = 172.80 sekunde Step 2: Kokotoa jumla ya muda uliotumika kwenye mabadilishano ya vijiti. Kuna mabadilishano 3 ya vijiti (kutoka A hadi B, B hadi C, na C hadi D). Kila mabadilishano huchukua sekunde 1. Muda wa mabadilishano = 3 × 1 = 3 sekunde Step 3: Kokotoa jumla ya muda wa mbio. Jumla ya muda wa mbio = Jumla ya muda wa kukimbia + Muda wa mabadilishano Jumla ya muda wa mbio = 172.80 + 3 = 175.80 sekunde Badilisha muda huu kuwa dakika na sekunde: 175.80 sekunde = 2 dakika na 55.80 sekunde Step 4: Kokotoa muda wa kuanza mbio kwa kutoa jumla ya muda wa mbio kutoka muda wa kumaliza. Muda wa kumaliza: 8:24:36 p.m. Muda wa mbio: 2 dakika 55.80 sekunde. Ili kutoa, tunahitaji kukopa kutoka dakika: 8:24:36.00 p.m. 0:02:55.80 Kukopa 1 dakika (60 sekunde) kutoka 24 dakika: 8:23:(36.00 + 60.00) p.m. = 8:23:96.00 p.m. Sasa toa: 8:23:96.00 p.m. 0:02:55.80 Muda wa kuanza = 8:21:40.20 p.m. Muda walioanza mbio ni 8:21:40.20 p.m.. 15. Panua na rahisha: (3x - 2y)^2 - (2y + 3x)^2 Step 1: Tumia fomula ya tofauti ya miraba, A^2 - B^2 = (A - B)(A + B). Hapa, A = (3x - 2y) na B = (2y + 3x). Step 2: Kokotoa (A - B). A - B = (3x - 2y) - (2y + 3x) A - B = 3x - 2y - 2y - 3x A - B = (3x - 3x) + (-2y - 2y) A - B = 0 - 4y = -4y Step 3: Kokotoa (A + B). A + B = (3x - 2y) + (2y + 3x) A + B = 3x - 2y + 2y + 3x A + B = (3x + 3x) + (-2y + 2y) A + B = 6x + 0 = 6x Step 4: Zidisha matokeo ya Step 2 na Step 3. (A - B)(A + B) = (-4y)(6x) = -24xy Kupanua na kurahisisha hutoa -24xy. 3 done, 2 left today. You're making progress.

In a 4 by 400 metres relay race, athletes A, B, C and D took 42.91 seconds, 42.95 seconds, 43.11 and 43.06 seconds respectively to do their race. An average of one second is spent on each button exchange. Calculate the time they started the race if they completed at 8:24:36 p.m.

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In a 4 by 400 metres relay race, athletes A, B, C and D took 42.91 seconds, 42.95 seconds, 43.11 and 43.06 seconds respectively to do their race. An average of one second is spent on each button exchange. Calculate the time they started the race if they completed at 8:24:36 p.m.

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