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

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 1. A cyclist travels a distance of 120 km from Town A to Town B at an average speed of x km/h. if he increases his average speed by 1 km/h, he would have saved 30 minutes. Find x.      Log On

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Question 389588: 1. A cyclist travels a distance of 120 km from Town A to Town B at an average speed of x km/h. if he increases his average speed by 1 km/h, he would have saved 30 minutes. Find x.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
t = d / r ___ the time for the faster rate is 1/2 hr less

120 / x = [120 / (x + 1)] + 1/2

multiplying by LCD [2x(x+1)] ___ 240x + 240 = 240x + x^2 + x

0 = x^2 + x - 240

factoring ___ 0 = (x + 16)(x - 15)

x + 16 = 0 ___ x = -16 ___ negative value not realistic

x - 15 = 0 ___ x = 15