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Train stations A, B and C are along a straight track. B is the middle of A and C. At 8.12am, RailExpress train leaves B and travels towards A at 60km/h. At 8.15am, Choot Train Sevicesleaves B and travels towards C at 75km/h. How far apat are they at 8.25am? Assume theyhave not reached their destinations.10. Sarah lives on the same street as Mandy, their homes are 202m apat. Sarah walks at 4m/stowards Mandy’s house. 12 seconds later, Mandy walks at 3m/s towards Sarah’s house. Howfar from Sarah’s house do they meet?1 min 12sA1min 30sB2 min 15sC2 min 30sDNone of theseE12.05pmA12.06pmB12.09pmC12.12pmDNone of theseE20 kmA22.5 kmB25.0 kmC25.5 kmDNone of theseE66mA102mB136mC192mDNone of theseE

Question

Train stations A, B and C are along a straight track. B is the middle of A and C. At 8.12am, RailExpress train leaves B and travels towards A at 60km/h. At 8.15am, Choot Train Se�vicesleaves B and travels towards C at 75km/h. How far apa�t are they at 8.25am? Assume theyhave not reached their destinations.10. Sarah lives on the same street as Mandy, their homes are 202m apa�t. Sarah walks at 4m/stowards Mandy’s house. 12 seconds later, Mandy walks at 3m/s towards Sarah’s house. Howfar from Sarah’s house do they meet?1 min 12sA1min 30sB2 min 15sC2 min 30sDNone of theseE12.05pmA12.06pmB12.09pmC12.12pmDNone of theseE20 kmA22.5 kmB25.0 kmC25.5 kmDNone of theseE66mA102mB136mC192mDNone of theseE

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Solution

It seems like there are multiple questions in your text. Let's break them down one by one:

  1. Train stations A, B and C are along a straight track. B is the middle of A and C. At 8.12am, RailExpress train leaves B and travels towards A at 60km/h. At 8.15am, Choot Train Services leaves B and travels towards C at 75km/h. How far apart are they at 8.25am? Assume they have not reached their destinations.

  2. Sarah lives on the same street as Mandy, their homes are 202m apart. Sarah walks at 4m/s towards Mandy’s house. 12 seconds later, Mandy walks at 3m/s towards Sarah’s house. How far from Sarah’s house do they meet?

Let's solve them:

  1. The RailExpress train has been traveling for 13 minutes (from 8.12am to 8.25am), or 13/60 = 0.2167 hours. In this time, it covers a distance of 60km/h * 0.2167h = 13km.

    The Choot Train Services has been traveling for 10 minutes (from 8.15am to 8.25am), or 10/60 = 0.1667 hours. In this time, it covers a distance of 75km/h * 0.1667h = 12.5km.

    Therefore, the two trains are 13km + 12.5km = 25.5km apart at 8.25am. So, the answer is (D) 25.5 km.

  2. Sarah has been walking for (12 seconds + the time it takes for them to meet) when they meet. Mandy has been walking for the time it takes for them to meet.

    If we let the time it takes for them to meet be t (in seconds), then the distance Sarah walks is 4m/s * (12s + t) and the distance Mandy walks is 3m/s * t.

    Since they start 202m apart, the sum of the distances they walk is 202m. So, we can set up the equation 4m/s * (12s + t) + 3m/s * t = 202m.

    Solving this equation for t gives t = 34 seconds. Therefore, the distance from Sarah's house where they meet is 4m/s * (12s + 34s) = 184m.

    So, the answer is not in the options given. It should be 184m.

This problem has been solved

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