chuck cycles skyline drive .
he cycles 60 km at an average speed of x km/h
he then cycles a further 45 km at an average speed of (x+4) km/h.
his total journey time is 6 hours .
write doun an eqn in x and shoe that it implifies to 2x^2-27x-80=0.

Question

chuck cycles skyline drive . 
he cycles 60 km at an average speed of x km/h
he then cycles a further 45 km at an average speed of (x+4) km/h.
his total journey time is 6 hours .
write doun an eqn in x and shoe that it implifies to 2x^2-27x-80=0.

mathstudent55 · Answer

$speed = \dfrac{distance}{time} $

$time = \dfrac{distance}{speed} $

$\dfrac{60}{x} + \dfrac{45}{x + 4} = 6$

$\dfrac{60}{x}\times \dfrac{x+4}{x+4} + \dfrac{45}{x + 4} \times \dfrac{x}{x}= 6$

$\dfrac{60(x + 4) + 45x}{(x + 4)x} = 6$

$60x + 240 + 45x = 6x^2 + 24x$

$6x^2 - 81x - 240 = 0$

$2x^2 - 27x - 80 = 0$