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Word problems and liner equations

  1. Sep 20, 2006 #1
    Can someone please help me with this question?

    Kareem took 5 h to drive 470km from Sudbury to Brantford. For part of the trip, he drove at 100 km/h. For the rest of the trip, he drove at 90 km/h. How far did he drive at each speed?

    I have to put it in linear equations.

    I think it is x+y= 470 and 100x+90y= 470

    The answer is 200 at 100 km/h and 270 at 90 km/h.

    But how do I get those numbers, by using substitution???????
  2. jcsd
  3. Sep 20, 2006 #2
    Hello caprija.

    The proper equations are

    100x + 90y = 470 where x is the number of hours driven at 100km/h and y is the number of hours driven at 90 km/h

    x + y = 5 in the problem it says that the total time he took was 5 hours (this is the equation you messed up)

    To solve by substitution you can solve for y in the 2nd equation
    x + y = 5
    y = 5 - x

    so now we know that y = 5 - x , so in the first equation we can put that expression in place of y

    100x + 90y = 470
    100x + 90(5-x) = 470
    100x + 450 - 90x = 470
    10x = 20
    x = 2

    x = 2 which means that the number of hours he drove at 100 km/h is 2, which means the number of hours he drove at 90km/h is 3.

    The problem asks for how many km he drove at each speed so simply take the hours and multiply them by the speed.

    100km/h*2 hours = 200 km
    90km/h*3 hours = 270 km

    hope this helps!
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