A cyclist travels at a distance of 120km from Town A to Town B at an average speed of x km/h. If he increases his speed by 1 km/h, he would have saved 30 minutes. Find x.

Question

perl · Answer

distance = (average rate) * (time elapsed)

120 = x * t   
120 = (x+1) (t - .5) 

solve this system

jjuden · Answer

120/x+1 = 120/x - 1/2h 
120/x+1 = 240-x/2x 
240x = (240-x)(x+1) 
240x = 240x + 240 - x^2 -x 
x+x^2 = 240 
15+15^2 = 240 
therefore x= 15

jjuden · Answer

orr
x= (-1 + sqrt(1^2 - 4(1)(-240)))/(2*1) 
x= (-1 + sqrt(961)) / 2 
x= (-1 + 31) /2 
x= 30/2 = 15

perl · Answer

do you have any questions?

perl · Answer

distance = (average rate) * (time elapsed)

120 = x * t 
120 = (x+1) (t - 1/2) 

to solve this system, solve for t in the first equation
t = 120/x 

then
120 = (x+1)( 120/x - 1/2) 

then distribute 

120 = x*120/x + 120/x - x/2 - 1/2

120 = 120 + 120/x - x/2 - 1/2

0 = 120/x - x/2 - 1/2

multiply both sides by 2x

0 = 240 - x^2 - x 

0 = (x - 15)(x+16) 

0 = 240 - x^2 - 2x