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How many kilometers did he cover in the first 2 hours?

Mathematics

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here are the solutions to the questions based on the graph:

IV) How many kilometers did he cover in the first 2 hours?

  1. The journey started at 8:00 AM.

    The first 2 hours would be from 8:00 AM to 10:00 AM.

  2. Looking at the graph, at 10:00 AM, the distance covered is 40 km.

    The cyclist covered:

    40 km\boxed{\text{40 km}}

    V) How long did he take to travel 50km?

  3. From the graph, the cyclist covered the first 40 km in 2 hours (from 8:00 AM to 10:00 AM).

  4. The remaining distance to reach 50 km is 50 km−40 km=10 km50 \text{ km} - 40 \text{ km} = 10 \text{ km}.

  5. After a rest period, the cyclist resumed travel at 11:00 AM from 40 km.

    The speed during this final segment (from 11:00 AM to 12:00 PM) is calculated as:

    Speed=Distance coveredTime taken=72 km−40 km12:00 PM−11:00 AM=32 km1 hour=32 km/h\text{Speed} = \frac{\text{Distance covered}}{\text{Time taken}} = \frac{72 \text{ km} - 40 \text{ km}}{12:00 \text{ PM} - 11:00 \text{ AM}} = \frac{32 \text{ km}}{1 \text{ hour}} = 32 \text{ km/h}

  6. Calculate the time taken to cover the remaining 10 km at this speed

    Time=DistanceSpeed=10 km32 km/h=1032 hours=516 hours\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{10 \text{ km}}{32 \text{ km/h}} = \frac{10}{32} \text{ hours} = \frac{5}{16} \text{ hours}

  7. Convert the fractional hours to minutes

    516×60 minutes=30016 minutes=18.75 minutes\frac{5}{16} \times 60 \text{ minutes} = \frac{300}{16} \text{ minutes} = 18.75 \text{ minutes}

  8. Add the time for the first 40 km and the time for the next 10 km to get the total travel time (excluding rest).

    Total travel time = 2 hours + 18.75 minutes.
    The cyclist took:

    2 hours and 18.75 minutes\boxed{\text{2 hours and 18.75 minutes}}

    VI) At what speed was the cyclist travelling between town P and town Q?

  9. Town P is the starting point (0 km) and Town Q is the end point (72 km).

  10. The total distance covered from Town P to Town Q is 72 km.

  11. The total time elapsed from the start (8:00 AM) to the end (12:00 PM) is 4 hours.

  12. Calculate the average speed for the entire journey

    Average Speed=Total DistanceTotal Time=72 km4 hours=18 km/h\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{72 \text{ km}}{4 \text{ hours}} = 18 \text{ km/h}

    The cyclist was travelling at an average speed of:

    18 km/h\boxed{\text{18 km/h}}
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