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In a triathlon, a contestant swims 5 km, cycles 30 km, and then runs 20 km. In general, a contestant runs at an average speed of x, swimsat an average speed of x/5, and cycles at an average speed of 5x, where x is in kilometres per hour.

a) Determine an expression for the total time taken to complete the race. (2 marks)
b) Cynthia can swim at 2 km/h. How long will it take her to complete the race? (1 mark)
c) If Shaitha can cycle at 40 km/h, how much longer will it take her to complete the race, compared to Cynthia? (1 mark)

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1 answer

  1. time = distance/speed

    5/(x/5) + 30/(5x) + 20/x
    = 25/x + 6/x + 20/x

    = 51/x

    she has gone 5 + 30 + 20 = 55 km

    b)
    2 = x/5
    so x = 10
    and time = 51/10 = 5.1 hr

    c)
    40 = 5x
    x = 8
    time = 51/8 = 6.375
    difference = 6.375 - 5.1 = 1.275

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