Question 560361
Fred cycled from home to his friends house and back again.
The distance from Fred's home to his friends house is 20km
on his way from home to his friends house fred cycled at Xkm per hour
on his way back freds speed had decreased by 2 km per hour
it took fred 4 hours altogether to cycle to his friends house and back.
Write down an equation for x.
:
Let x = from home speed
then
(x-2) = return home speed
:
Write a time equation, time = dist/speed
:
from time + return time = 4 hrs
{{{20/x}}} + {{{20/((x-2))}}} = 4
multiply by x(x-2) to clear the denominators, results:
20(x-2) + 20x = 4x(x-2)
20x - 40 + 20x = 4x^2 - 8x
combine like terms on the right
0 = 4x^2 - 8x - 40x + 40
A quadratic equation
4x^2 - 48x + 40 = 0
simplify, divide by 4 and you have
x^2 - 12x + 10 = 0
and solve it.
Use the quadratic formula: a=1, b=-12; c=10
Only one solution will make sense, check it in the original time equation