I don't seem to be getting the questions that involve the manipulation of speed = distance/time. Here's the question I'm stuck with in particular:
"A man has to travel 50km in 4 hours. He does it by walking the first 7km at x km/h, cycling the next 7km at 4x km/h and motoring the remainder at (6x + 3) km/h. Find x."

    JJJJJJJJJJ
    Hey JJJJJJJJJJ,

    I'm sure there are a few different approaches to this question but here is my one:
    One thing to note about speed-distance-time questions is that if you divide the distance by the speed, you will get time (i.e. hours).

    So, to summarise the information in the question:
    Walking - 7km at x km/hr
    Cycling - 7 km at 4x km/hr
    Motoring - 36km at (6x + 3) km/h
    TOTAL: 50 km in 4 hours
    This means that 7km/x + 7km/4x + 36km/(6x+3) = 4 hours, due to the note I stated above (I left out the km/hr units so that it's not confusing).
    So, now you have to do a bit of algebraic gymnastics which I will leave out for the sake of your sanity (however, please do let me know if you would like the working out for this part) and you should get this:
    96x2 - 306x - 105 = 0
    With some factorisation, you should get 3(16x + 5)(2x - 7) = 0 and due to the null factor law, this means that
    x = -5/16 and 7/2
    Since x > 0, x = -5/16 is an extraneous solution and therefore, x = 7/2 = 3.5.
    You can use this x value to sub back into the original question to check if it's correct.

    Hope this helps and let me know if you need more working out or explanation.

    • PP
      a month later

      Anyone got practice test for METHODS YEAR 10? TIA

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