The distance between Town A and Town B is 1260 km. Train X travels from Town A to Town B at 8.00 a.m. at an average speed of 230 km/h. At the same time, Train Y travels from Town B to Town A at an average speed of 190 km/h.

  1. (a)

    What time did they meet?

    Answer: (a) ___

  2. (b)

    How far would each train have travelled when they meet on the way?

    1. (b(i))

      Train X: ___

    2. (b(ii))

      Train Y: ___

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Worked solution

9(a)

1. Calculate the relative speed of the two trains

Relative speed = 230+190=420230 + 190 = 420 km/h

2. Calculate the time taken for the trains to meet

Time taken = 1260420=3\frac{1260}{420} = 3 hours

3. Determine the meeting time

Meeting time = 3 hours after 8.00 a.m. = 11.00 a.m.

Answer

11.00 a.m.

9(b)(b(i))

1. Find the time taken for the two trains to meet

Relative speed=230+190=420 km/h\text{Relative speed} = 230 + 190 = 420\text{ km/h}
Time taken=1260420=3 hours\text{Time taken} = \frac{1260}{420} = 3\text{ hours}

2. Calculate the distance travelled by Train X

Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}
Distance=230×3=690 km\text{Distance} = 230 \times 3 = 690\text{ km}

Answer

690 km690\text{ km}

9(b)(b(ii))

1. Determine the time taken for the trains to meet (from part a)

Relative speed=230+190=420 km/h\text{Relative speed} = 230 + 190 = 420\text{ km/h}
Time taken=1260420=3 hours\text{Time taken} = \frac{1260}{420} = 3\text{ hours}

2. Calculate the distance travelled by Train Y

Distance=Speed×Time=190×3=570 km\text{Distance} = \text{Speed} \times \text{Time} = 190 \times 3 = 570\text{ km}

Answer

570 km570\text{ km}

AI analysis — may contain mistakes.

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