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anonymous

  • one year ago

A car journey of 380 km lasts 4 hours. Part of this is on a motorway at an average speed of 110kmh^-1, the rest on country roads at an average speed of 70kmh^-1. (i) Write this information as pair of simultaneous equations. (ii) Solve you equations to find how many kilometres of the journey is spent on each type of road. So, I know what the answers are but I can't figure out how to get to it myself. Please will you help by showing me how?

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  1. welshfella
    • one year ago
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    use the relation v = d/t v= speed , d = distance travel on a motorway and t = time taken on the motorway so for motorway travel we have 110 = d/t and for the country roads 70 = (380 - d) / (4 - t)

  2. welshfella
    • one year ago
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    so there are your 2 equations

  3. welshfella
    • one year ago
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    writing the equation without fractions we get d = 110t 380 - d = 70(4 - t) to solve for t substitute d = 110t in the second equation 380 - 110t = 280 - 70t 380 - 280 = 110t - 70t can you continue with this?

  4. welshfella
    • one year ago
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    oh they want number of kilometers on each type of road I should have solved for d no matter when we find t we can then plug in the values to find the distances

  5. welshfella
    • one year ago
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    fo you follow it OK so far?

  6. welshfella
    • one year ago
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    are you there?

  7. anonymous
    • one year ago
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    Yes, I am just a bit confused since those are not the answers my book got? I will give those too you now...

  8. anonymous
    • one year ago
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    t(subscript 1) + t(subscript 2) =4; 110t(subscript 1) + 70t(subscript 2) = 380 Sorry I cant type the subscript numbers on my computer.

  9. anonymous
    • one year ago
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    That is what my textbook has said are the answers to the first question.

  10. welshfella
    • one year ago
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    yes thats basically the same as i have bu they have called the two times t1 and t2 whereas ive called them t and 4 - t because total time was 4 hours

  11. welshfella
    • one year ago
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    if you solve for t you;ll find t = time for motoirway journey = 2.5 hours and so time foe road journey = 4-2.5 = 1.5 and distance for motorway = 110 * 2.5 = 275km and for raoad = 70 8 1.5 = 105 km

  12. welshfella
    • one year ago
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    t1 + t1 = 4 110 t1 + 70 t2 = 380 is what your book has said

  13. welshfella
    • one year ago
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    do you want me to show you how to solve this?

  14. welshfella
    • one year ago
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    there is often a few different ways to solve problems like this.

  15. anonymous
    • one year ago
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    Oh ok. I think I understand now- thank you very much!

  16. welshfella
    • one year ago
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    oh that should be t1 + t2 = 4

  17. welshfella
    • one year ago
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    yw

  18. welshfella
    • one year ago
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    t1 being time for motorway and t2 time for roads

  19. anonymous
    • one year ago
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    Ok. You have helped me a lot!

  20. welshfella
    • one year ago
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    yw

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