# 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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