Question 1029152
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A biker decided to cover the distance of 120 km at a certain speed. However, he actually went 6 km/h slower 
so he arrived at his destination 1 hour later than he wanted to. What was the actual speed of the biker?
PS:If x is the actual speed of the biker, then what is the equation?
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<pre>
Let x be the actual speed of the biker, in {{{km/h}}}.
Then his planned speed was (x+6).

So he planned to spend {{{120/(x+6)}}} hours, but actually spent {{{120/x}}}, which is in 1 hour more.

Thus you have this equation

{{{120/x}}} - {{{120/(x+6)}}} = 1.

To solve it for x , multiply both sides by x*(x+6). You will get

120*(x+6) -120x = x*(x+6),   or

120*6 = x*(x+6),   or

{{{x^2 + 6x - 720}}} = {{{0}}}.

Factor left sides:

(x-24)*(x+30) = 0.

The roots are  x = 24  and  x = -30.
Only positive x = 24 fits.

<U>Answer</U>.  The actual speed of the biker is 24 {{{km/h}}}. 

Please check it yourself.
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