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a cyclist travels a distance of 120 km from town A to town B at an average speed of xkm/h. If he increase his average speed by 1 km/h he would save 30 min. find x

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Donna B. | Specializing in GRE, SAT prep!!Specializing in GRE, SAT prep!!
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D=rt so 120 = xt for the first part of the problem.  Therefore, t = 120/x.  Using the increased speed, your new equation becomes 120 = (x + 1)(120/x - 1/2)  because (x + 1) is the new speed and (120/x - 1/2) is the new time.  Using your best algebra skills you can simplify this second equation eventually to x2 + x - 240 = 0  which factors into (x + 16)(x - 15) = 0.  Solving this, x = -16 or x = 15 and you can throw out the first because it's negative.  Therefore, x = 15km/h.

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