math

A cyclist travels for 60km at x km/h and 180km at y km/h and takes 10 hours altogether for the journey. If the speed are interchange, the journey takes 8.6 (8 whole number 2 over 3) hours. Find x and y.

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  1. 60 + 180 = 140 km journey length
    time at x = 60/x
    time at y = 180/y
    total time = 60/x + 180/y = 10

    now interchange
    total time = 180/x + 60/y = 8 2/3 = 26/3

    two equations
    60 y + 180 x = 10 x y
    180 y + 60 x = 26 x y /3
    multiply bottom equation by 3
    60 y + 180 x = 10 x y and
    540y + 180 x = 26 x y
    ---------------------------subtract
    -480 y = -16 x y
    x = 30
    etc

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  2. Thank you very much Damon :)

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  3. The ages of a man and a woman are ratio 5:4.In 12 years time the ratio of their ages will be 19:16.How old are they now

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  4. Man's age presently =5a
    Woman's age presently = 4a
    In 12yrs time :
    Man's age = 5a+12
    Woman's age = 4a+12

    ...5a+12:4a+12= 19: 16
    5a+12/4a+12=19/16
    ...a = 9

    ....Man's present age = 5a = 5(9)=45yrs
    .....Woman's present age = 4a=4(9)=36yrs

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  5. A woman borrows £180,000 from a bank at 10% per annum compound interest. She repays 50,000 at the end of each year. How much does she still owe at the end of 4 years?

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