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Kagwa and Manzi are traveling towards each other from Town A and Town B respectively. Town A and Town B are 520 km apart. Kagwa starts at 7:00 am, traveling at 80 km/hr. Manzi starts at 9:00 am, trave

Mathematics

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3 parts
a

11:00 am\text{11:00 am}

b

320 km320 \text{ km}

c

200 km200 \text{ km}

Step-by-step solution

9 steps

Here are the solutions to the problem:

Part a· 5 steps

At which time did Kagwa and Manzi meet?

  1. Calculate the distance Kagwa covered before Manzi started.

    Kagwa started at 7:00 am and Manzi started at 9:00 am.
    Time difference = 9:00 am−7:00 am=2 hours9:00 \text{ am} - 7:00 \text{ am} = 2 \text{ hours}.
    Distance covered by Kagwa in 2 hours:

    Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time} DistanceKagwa initial=80 km/hr×2 hr=160 km\text{Distance}_{\text{Kagwa initial}} = 80 \text{ km/hr} \times 2 \text{ hr} = 160 \text{ km}
  2. Calculate the remaining distance between them when Manzi started.

    Total distance between Town A and Town B is 520 km.
    Remaining distance = Total distance - Distance Kagwa initial

    Remaining distance=520 km−160 km=360 km\text{Remaining distance} = 520 \text{ km} - 160 \text{ km} = 360 \text{ km}
  3. Calculate their relative speed.

    Since they are moving towards each other, their speeds add up.

    Relative speed=SpeedKagwa+SpeedManzi\text{Relative speed} = \text{Speed}_{\text{Kagwa}} + \text{Speed}_{\text{Manzi}} Relative speed=80 km/hr+100 km/hr=180 km/hr\text{Relative speed} = 80 \text{ km/hr} + 100 \text{ km/hr} = 180 \text{ km/hr}
  4. Calculate the time it took for them to meet after Manzi started.

    Time to meet=Remaining distanceRelative speed\text{Time to meet} = \frac{\text{Remaining distance}}{\text{Relative speed}} Time to meet=360 km180 km/hr=2 hours\text{Time to meet} = \frac{360 \text{ km}}{180 \text{ km/hr}} = 2 \text{ hours}
  5. Determine the meeting time.

    They met 2 hours after Manzi started (9:00 am).

    Meeting time=9:00 am+2 hours=11:00 am\text{Meeting time} = 9:00 \text{ am} + 2 \text{ hours} = 11:00 \text{ am}

    The time Kagwa and Manzi met is 11:00 am\boxed{\text{11:00 am}}.

Part b

320 km320 \text{ km}

Find the distance covered by Kagwa.

  1. Calculate the total time Kagwa traveled until they met.

    Kagwa traveled for 2 hours before Manzi started, and then another 2 hours until they met.

    Total time Kagwa traveled=2 hours+2 hours=4 hours\text{Total time Kagwa traveled} = 2 \text{ hours} + 2 \text{ hours} = 4 \text{ hours}
  2. Calculate the distance covered by Kagwa.

    DistanceKagwa=SpeedKagwa×Total time Kagwa traveled\text{Distance}_{\text{Kagwa}} = \text{Speed}_{\text{Kagwa}} \times \text{Total time Kagwa traveled} DistanceKagwa=80 km/hr×4 hours=320 km\text{Distance}_{\text{Kagwa}} = 80 \text{ km/hr} \times 4 \text{ hours} = 320 \text{ km}

    The distance covered by Kagwa is 320 km\boxed{320 \text{ km}}.

Part c

200 km200 \text{ km}

Find the distance covered by Manzi.

  1. Calculate the total time Manzi traveled until they met.

    Manzi started at 9:00 am and they met at 11:00 am.

    Total time Manzi traveled=11:00 am−9:00 am=2 hours\text{Total time Manzi traveled} = 11:00 \text{ am} - 9:00 \text{ am} = 2 \text{ hours}
  2. Calculate the distance covered by Manzi.

    DistanceManzi=SpeedManzi×Total time Manzi traveled\text{Distance}_{\text{Manzi}} = \text{Speed}_{\text{Manzi}} \times \text{Total time Manzi traveled} DistanceManzi=100 km/hr×2 hours=200 km\text{Distance}_{\text{Manzi}} = 100 \text{ km/hr} \times 2 \text{ hours} = 200 \text{ km}

    The distance covered by Manzi is 200 km\boxed{200 \text{ km}}.

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