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.

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

Thank you very much Damon :)

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

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?

To solve this problem, we can use the formula Time = Distance / Speed.

Let's consider the first part of the journey, where the cyclist travels 60 km at a speed of x km/h. According to the given information, the time taken for this part is given by:

Time1 = 60 km / x km/h

Similarly, for the second part of the journey where the cyclist travels 180 km at a speed of y km/h, the time taken is:

Time2 = 180 km / y km/h

According to the problem, the total time taken for the journey is 10 hours. So, we can write the first equation:

Time1 + Time2 = 10

Now, if the speeds are interchanged, the total time taken for the journey becomes 8 2/3 hours. In this case, the time taken for the first part is:

Time1' = 60 km / y km/h

And the time taken for the second part is:

Time2' = 180 km / x km/h

We can write the second equation based on this information:

Time1' + Time2' = 8 2/3

Now, we have two equations with two unknowns (x and y). We can solve these equations using substitution or elimination method:

Equation 1: Time1 + Time2 = 10

Equation 2: Time1' + Time2' = 8 2/3

Substituting the values of Time1, Time2, Time1', and Time2' derived earlier:

(60/x) + (180/y) = 10

(60/y) + (180/x) = 26/3

To simplify the equations, we can multiply both sides of Equation 1 by xy and Equation 2 by 3xy:

180y + 60x = 10xy ........(3)

180x + 60y = 26xy ........(4)

Now, we can solve these two equations simultaneously to find the values of x and y.

Multiplying Equation 4 by 3 and Equation 3 by 26 gives:

540x + 180y = 78xy ........(5)

1560x + 360y = 260xy ........(6)

Subtracting Equation 5 from Equation 6:

(1560x + 360y) - (540x + 180y) = (260xy - 78xy)

1020x + 180y = 182xy

Dividing both sides of the equation by 2:

510x + 90y = 91xy ........(7)

Substituting Equation 3 into Equation 7:

510x + 90(10xy - 60x) = 91xy

510x + 900xy - 540x = 91xy

-30x = -809xy

Simplifying and rearranging:

30x = 809xy

Dividing both sides by x:

30 = 809y

Solving for y:

y = 30 / 809

Similarly, substituting y back into Equation 3:

60 / x + 180 / (30 / 809) = 10

Multiply both sides by x:

60 + (180 * (809 / 30)) = 10x

Simplify:

60 + 4,852 = 10x

4,912 = 10x

Divide both sides by 10:

491.2 = x

Therefore, the values of x and y are approximately x = 491.2 and y = 0.0371.

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