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A motorcyclist left town X for Y. He rested at Y for half an hour and continued to Z, which is 80km away from Y, for 1½ hours. He rested at Z for one hour and returned at a speed of 70km/h. Complete the motorcyclist's journey.

Mathematics

ScanSolve AI Answer

Answer

b

08:30\text{08:30}

Step-by-step solution

3 steps

Huu hapa ni ufumbuzi wa swali lako:

Part a

Kamilisha safari ya mwendesha pikipiki.

Ili kukamilisha grafu, fuata hatua hizi:

  • Kupumzika Y: Mwendesha pikipiki alifika Y saa 8:00 asubuhi (kilomita 60 kutoka X). Alipumzika kwa nusu saa. Hivyo, chora mstari ulionyooka mlalo kutoka (8:00 asubuhi, 60 km) hadi (8:30 asubuhi, 60 km).
  • Kusafiri Y hadi Z: Aliondoka Y saa 8:30 asubuhi na kusafiri kilomita 80 hadi Z kwa saa 1121\frac{1}{2}.
    • Umbali wa Z kutoka X ni 60 km+80 km=140 km60 \text{ km} + 80 \text{ km} = 140 \text{ km}.
    • Muda wa kufika Z ni 8:30 asubuhi+1 saa 30 dakika=10:00 asubuhi8:30 \text{ asubuhi} + 1 \text{ saa } 30 \text{ dakika} = 10:00 \text{ asubuhi}.
    • Chora mstari kutoka (8:30 asubuhi, 60 km) hadi (10:00 asubuhi, 140 km).
  • Kupumzika Z: Alipumzika Z kwa saa moja. Hivyo, chora mstari ulionyooka mlalo kutoka (10:00 asubuhi, 140 km) hadi (11:00 asubuhi, 140 km).
  • Kurudi X: Aliondoka Z saa 11:00 asubuhi na kurudi X (kilomita 0) kwa kasi ya 70 km/h.
    • Muda wa kurudi ni 140 km70 km/h=2 saa\frac{140 \text{ km}}{70 \text{ km/h}} = 2 \text{ saa}.
    • Muda wa kufika X ni 11:00 asubuhi+2 saa=1:00 mchana11:00 \text{ asubuhi} + 2 \text{ saa} = 1:00 \text{ mchana}.
    • Chora mstari kutoka (11:00 asubuhi, 140 km) hadi (1:00 mchana, 0 km).

Part b

08:30\text{08:30}

Eleza muda mwendesha pikipiki aliondoka mji Y katika saa ya saa 24.

  1. Pata muda aliofika Y na muda alipumzika.

    Mwendesha pikipiki alifika Y saa 8:00 asubuhi.
    Alipumzika kwa nusu saa (dakika 30).

  2. Kokotoa muda aliondoka Y.

    Muda aliondoka Y ni 8:00 asubuhi+30 dakika=8:30 asubuhi8:00 \text{ asubuhi} + 30 \text{ dakika} = 8:30 \text{ asubuhi}.

  3. Badilisha muda kuwa saa ya saa 24.

    Katika saa ya saa 24, 8:30 asubuhi ni 08:30.

    Muda mwendesha pikipiki aliondoka mji Y katika saa ya saa 24 ni:

    08:30\boxed{\text{08:30}}
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