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Math Help - Urgently need help with alebra problem!!

  1. #1
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    Urgently need help with alebra problem!!

    Hi
    My 15 year old daughter urgently needs help with two algebra problems for her year 10 maths. We would be very grateful if someone could show us how to solve the following two problems.


    1)
    A school is expected to plant trees along a river bank. The project is to take a certain number of days.
    If they plant 240 trees per day, then they will be short by 400 trees.
    If they plant 280 trees per day, they will plant 200 more than planned.
    How many trees are planted, and how many days will it take?
    2)A train passes a pole in 15 seconds, and in 45 seconds it passes through a tunnel 600 metres long. What is the speed of the train? How long is it?
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  2. #2
    Member
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    Aug 2007
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    Hi, jennybianca

    1) Firstly we need to set up the equations.

    Let~D~=~Number~of~Days~~~,~~~P~=~Total~Planned~Tre  es

    "If they plant 240 trees per day, then they will be short by 400 trees."

    So;

    240D~=~P-400~~~[1]

    "If they plant 280 trees per day, they will plant 200 more than planned."

    So;

    280D~=~P+200~~~[2]

    No solve [1] and [2] simultaneously.

    [1]~~~P~=~240D+400

    [2]~~~P~=~280D-200

    Thus,

    240D+400~=~280D-200

    \implies~40D~=~600

    \implies~D~=~15

    Now sub into either [1] or [2] to find out how many trees planned ( P)

    2) We have Time~=~t~=~45s~~~,~~~Distance~=~d~=~600m

    Now use the formula s~=~\frac{d}{t} (where s is the speed of the train)

    s~=~\frac{600}{45}

    \implies~s~=~\frac{40}{3}~\approx~13.33

    Now because we have metres over second the unit is metre per second (ms^{-1})

    Thus the speed of the train is \frac{40}{3}ms^{-1}~\approx~13.33ms^{-1}

    Now assuming the width of the pole is negligible and the train has constant speed, the same formula can be used;

    s~=~\frac{d}{t}

    \implies~d~=~st

    \implies~d~=~\frac{40}{3}\cdot15

    \implies~d~=~200

    Thus the length of the train is 200m
    Last edited by Sean12345; May 11th 2008 at 05:29 AM. Reason: Question 2
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  3. #3
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    This is fantastic. I showed my daughter your response & it helped her a great deal. The way you explained it & set it out is very professional. Thank you very much.
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