Consider a watch face which has identical hands and identical marks
for the hours. It is opposite to a mirror. When is the time as read
direct and in the mirror exactly the same between 6 and 7?
A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?
A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.
Let the height of the shorter candle be x and the height of the
taller candle be x + 3. Assume that the short candle burns down at
a cm per hour and the tall candle burns down at b cm per hour.
The candles are the same length at 9.30 so:
Also the short candle burns out after 4 hours so:
and the tall candle burns out after 6 hours so:
Using equations 1,2 and 3 gives rise to
x - 2.5x /4 =x +3 - 4(x+3)/6
which when solved gives x = 24cm
Finally, originally the shorter candle was 24cm and the longer
one was 27cm.