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Math Help - Simultaneous and linear equations

  1. #1
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    Simultaneous and linear equations

    A rower travels upstream at 6 km per hour and back to the starting place at 10 km per hour. The total journey takes 48 minutes. How far upstream did the rower go?


    A man travels from A to B at 4km/h and then from B and A at 6 km/h. The total journey takes 45 minutes. Find the distance travelled.
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  2. #2
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    Quote Originally Posted by delicate_tears View Post
    A rower travels upstream at 6 km per hour and back to the starting place at 10 km per hour. The total journey takes 48 minutes. How far upstream did the rower go?
    ...
    If
    v is the speed
    d is the distance
    t is the time
    then you are supposed to know that v=\frac dt

    Let x be the distance and y be the time rowing upstream then you have
    total time t = 0.8 h = 48 min
    rowing upstream: y
    rowing downstream 0.8 h - y

    \left| \begin{array}{r}6=\frac xy\\10 = \frac x{0.8-y}\end{array}\right. .... Multiply by the denominators: \left| \begin{array}{r}6y= x\\10(0.8-y) =  x \end {array} \right.

    Substitute x by 6y:

    8-10y = 6y~\iff~y=\frac12

    The rower needs half an hour to row upstream by a speed of 6 \frac{km}{h} that means the distance upstream is 3 km.
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  3. #3
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    Quote Originally Posted by delicate_tears View Post
    ...

    A man travels from A to B at 4km/h and then from B and A at 6 km/h. The total journey takes 45 minutes. Find the distance travelled.
    Let d be the distance between A and B.

    From v=\frac dt you get: t=\frac dv. With your problem:

    \frac d4 + \frac d6 = \frac34 .......... Multiply by 24:

    6d + 4d = 18~\iff~d=1.8

    The total distance is therefore 3.6 km
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