<PRE><B>Question 839167</B>
A cyclist travels a distance of 120km from Town A to Town B at an average speed of x km/h. If he increases his speed by 1km/h, he would save 30 minutes. Find x

Original Time - time after speed increase = 1/2 hour

{{{120/x - 120/(x+1) = 1/2}}}

multiply the equation by 2x(x+1)

we get

2*120(x+1) -2*120*x = x(x+1)

240x+240 -240x=x^2+x

x^2+x-240=0

x^2+16x-15x-240=0

x(x+16)-15(x+16)=0

(x+16)(x-15)=0

x cannot be negative
so x=15</PRE>