We read your photo as:

Two friends Ali and John live 40km apart. One day Ali left his house at 9.00 am and cycle towards John's house at an average speed of 15km/h. John left his house at 10.30 am on the same day and cycled towards Ali's at an average speed of 25km/h.

Mathematics

ScanSolve AI Answer

Step-by-step solution

10 steps

Here's the solution to question 7:

a) (i) Determine the distance from Ali's house, where the two friends met.

  1. Calculate the distance Ali traveled before John started.

    Ali started at 9:00 am, and John started at 10:30 am.
    Time difference = 10:30 am−9:00 am=1 hour 30 minutes=1.5 hours10:30 \text{ am} - 9:00 \text{ am} = 1 \text{ hour } 30 \text{ minutes} = 1.5 \text{ hours}.
    Distance Ali traveled in this time = Ali's speed ×\times Time

    DAli,initial=15 km/h×1.5 h=22.5 kmD_{Ali, initial} = 15 \text{ km/h} \times 1.5 \text{ h} = 22.5 \text{ km}

  2. Calculate the remaining distance between them when John started.

    Total distance between houses = 40 km.
    Remaining distance = Total distance - DAli,initialD_{Ali, initial}

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

  3. Calculate the time taken for them to meet after John started.

    Both are moving towards each other, so their relative speed is the sum of their speeds.
    Relative speed = Ali's speed + John's speed = 15 km/h+25 km/h=40 km/h15 \text{ km/h} + 25 \text{ km/h} = 40 \text{ km/h}.
    Time to meet (tmeett_{meet}) = Remaining distance / Relative speed

    tmeet=17.5 km40 km/h=17.540 hours=175400 hours=716 hourst_{meet} = \frac{17.5 \text{ km}}{40 \text{ km/h}} = \frac{17.5}{40} \text{ hours} = \frac{175}{400} \text{ hours} = \frac{7}{16} \text{ hours}

  4. Calculate the total distance Ali traveled from his house to the meeting point.

    Total distance Ali traveled = DAli,initial+Ali’s speed×tmeetD_{Ali, initial} + \text{Ali's speed} \times t_{meet}

    DAli,total=22.5 km+15 km/h×716 hD_{Ali, total} = 22.5 \text{ km} + 15 \text{ km/h} \times \frac{7}{16} \text{ h} DAli,total=22.5+10516=22.5+6.5625=29.0625 kmD_{Ali, total} = 22.5 + \frac{105}{16} = 22.5 + 6.5625 = 29.0625 \text{ km}

    The distance from Ali's house where they met is 29.0625 km\boxed{29.0625 \text{ km}}.

    a) (ii) The time they met.

  5. Convert tmeett_{meet} to minutes and seconds.

    tmeet=716 hours×60 minutes/hour=42016 minutes=26.25 minutest_{meet} = \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.

  6. Add this time to John's start time (when both were moving).

    Meeting time = 10:30 am + 26 minutes 15 seconds
    The time they met is 10:56:15 am\boxed{10:56:15 \text{ am}}.

    a) (iii) How far Ali was from John's house when they met.

    This is the distance John traveled from his house to the meeting point.
    Distance John traveled = John's speed ×tmeet\times t_{meet}

    DJohn,total=25 km/h×716 h=17516 km=10.9375 kmD_{John, total} = 25 \text{ km/h} \times \frac{7}{16} \text{ h} = \frac{175}{16} \text{ km} = 10.9375 \text{ km}

    Ali was 10.9375 km\boxed{10.9375 \text{ km}} from John's house when they met.

    b) The two friends took 10 minutes at the meeting point and then cycle to John's at an average speed of 12km/h. Find the time they arrived at John's house.

  7. Calculate the time they left the meeting point.

    Time they met = 10:56:15 am.
    Time spent at meeting point = 10 minutes.
    Time they left meeting point = 10:56:15 am + 10 minutes = 11:06:15 am.

  8. Calculate the time taken to cycle from the meeting point to John's house.

    Distance from meeting point to John's house = 10.9375 km10.9375 \text{ km} (from part a(iii)).
    New cycling speed = 12 km/h.
    Time taken = Distance / Speed

    tto_John=10.9375 km12 km/h=175/1612 hours=175192 hourst_{to\_John} = \frac{10.9375 \text{ km}}{12 \text{ km/h}} = \frac{175/16}{12} \text{ hours} = \frac{175}{192} \text{ hours}

  9. Convert tto_Johnt_{to\_John} to minutes and seconds.

    tto_John=175192 hours×60 minutes/hour=10500192 minutes≈54.6875 minutest_{to\_John} = \frac{175}{192} \text{ hours} \times 60 \text{ minutes/hour} = \frac{10500}{192} \text{ minutes} \approx 54.6875 \text{ minutes}

    This is 54 minutes and 0.6875×60=41.250.6875 \times 60 = 41.25 seconds. Rounding to the nearest second, this is 54 minutes and 41 seconds.

  10. Calculate the arrival time at John's house.

    Arrival time = Time they left meeting point + Time taken to cycle to John's house
    Arrival time = 11:06:15 am + 54 minutes 41 seconds
    Arrival time = 11: (06+54) : (15+41) am
    Arrival time = 11:60:56 am
    Since 60 minutes make an hour, this is 12:00:56 pm.
    The time they arrived at John's house is 12:00:56 pm\boxed{12:00:56 \text{ pm}}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QWhat is the equation of a circle with radius 5 and center (−3,2)?QSin(pi/3) cos(pi/6) + cos(pi/3) sin(pi/6)QFind without using tables, the values cos42° (cos18° - sin42° sin18°)QChange of subject and Real-world Application: The relationships between temperature in Celsius (C)…QComplete the table: Items, Price of each, Total expenses. 5kg of meat 3000frw/kg, 5kg of rice…
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.