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Two friends, Ojiwang and David, live 40 km apart. Ojiwang starts cycling towards David's house at 9:00 a.m. at a speed of 15 km/h. David starts cycling towards Ojiwang's house at 10:30 a.m. at a speed

Mathematics

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2 parts
i

26 minutes 15 seconds\text{26 minutes 15 seconds}

ii

10:56:15 a.m.\text{10:56:15 a.m.}

Step-by-step solution

6 steps

Here's the solution to question 16.

Part i· 5 steps

The time taken before the two friends met.

  1. Calculate the duration of Ojiwang's head start.

    Ojiwang started at 9:00 a.m.
    David started at 10:30 a.m.
    The time difference is 10:30 a.m.−9:00 a.m.=1 hour 30 minutes=1.5 hours10:30 \text{ a.m.} - 9:00 \text{ a.m.} = 1 \text{ hour } 30 \text{ minutes} = 1.5 \text{ hours}.

  2. Calculate the distance Ojiwang covered during his head start.

    Ojiwang's speed is 15 km/h15 \text{ km/h}.

    Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time} DOjiwang initial=15 km/h×1.5 h=22.5 kmD_{\text{Ojiwang initial}} = 15 \text{ km/h} \times 1.5 \text{ h} = 22.5 \text{ km}

  3. Determine the remaining distance between them when David started cycling.

    The total distance between their houses is 40 km40 \text{ km}.

    Dremaining=40 km−22.5 km=17.5 kmD_{\text{remaining}} = 40 \text{ km} - 22.5 \text{ km} = 17.5 \text{ km}

  4. Calculate their relative speed.

    Since they are cycling towards each other, their speeds add up.
    Ojiwang's speed is 15 km/h15 \text{ km/h}.
    David's speed is 25 km/h25 \text{ km/h}.

    Srelative=15 km/h+25 km/h=40 km/hS_{\text{relative}} = 15 \text{ km/h} + 25 \text{ km/h} = 40 \text{ km/h}

  5. Calculate the time taken for them to meet after David started.

    Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}} Tmeet=DremainingSrelative=17.5 km40 km/hT_{\text{meet}} = \frac{D_{\text{remaining}}}{S_{\text{relative}}} = \frac{17.5 \text{ km}}{40 \text{ km/h}} Tmeet=17.540 hours=175400 hours=716 hoursT_{\text{meet}} = \frac{17.5}{40} \text{ hours} = \frac{175}{400} \text{ hours} = \frac{7}{16} \text{ hours}

    To convert this to minutes and seconds:

    716 hours×60 minutes/hour=42016 minutes=26.25 minutes\frac{7}{16} \text{ hours} \times 60 \text{ minutes/hour} = \frac{420}{16} \text{ minutes} = 26.25 \text{ minutes}

    This is 26 minutes and 0.25×60=150.25 \times 60 = 15 seconds.

    The time taken before the two friends met (after David started) is 26 minutes 15 seconds\boxed{\text{26 minutes 15 seconds}}.

Part ii

10:56:15 a.m.\text{10:56:15 a.m.}

The time they met.

  1. Add the meeting time duration to David's starting time.

    David started at 10:30 a.m.
    They met 26 minutes and 15 seconds later.

    Meeting Time=10:30:00 a.m.+00:26:15\text{Meeting Time} = 10:30:00 \text{ a.m.} + 00:26:15 Meeting Time=10:56:15 a.m.\text{Meeting Time} = 10:56:15 \text{ a.m.}

    The time they met is 10:56:15 a.m.\boxed{\text{10:56:15 a.m.}}.

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