# SOLUTION: I've been working on word problems, but this one has me stumped. A car travels 120 miles. A second car; traveling 10 mph faster than the first car, makes the same trip in one hou

Algebra ->  -> SOLUTION: I've been working on word problems, but this one has me stumped. A car travels 120 miles. A second car; traveling 10 mph faster than the first car, makes the same trip in one hou      Log On

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 Click here to see ALL problems on Quadratic Equations Question 5211: I've been working on word problems, but this one has me stumped. A car travels 120 miles. A second car; traveling 10 mph faster than the first car, makes the same trip in one hour less time. Find the speed of each car.Found 2 solutions by xcentaur, glabow:Answer by xcentaur(357)   (Show Source): You can put this solution on YOUR website!distance travlled by first car=120 miles speed of first car=x mph time taken by first car=d/s=(120/x)hours speed of second car=(x+10)mph distance travelled=120 miles time taken=d/s=[120/(x+10)]hours Given,time taken by second car is one hour less than first car. then, 120/x-120/(x+10)=1 [120(x+10)-120x]/x(x+10)=1 [120x-120x+1200]/x(x+10)=1 1200/x(x+10)=1 1200=x(x+10) x^2+10x-1200=0 x^2+30x-40x-1200=0 x(x+30)-40(x+30)=0 (x+30)(x-40)=0 x=-30 or +40 Speed cannot be -ve. hence x=40 mph Thus speed of first car=40 mph,second car=50 mph Hope this helps, good luck. Answer by glabow(165)   (Show Source): You can put this solution on YOUR website!Always be careful and define the variables you are using. Let x = the speed of the first car Then x+10 = the speed of the second car Let t1 = the time the first car takes to travel 120 miles Then t2 = the time the second car takes to travel 120 miles We know that t1 = t2 + 1 (why?) The equation for time of travel is t = distance / speed For the two cars we have the following equations t1 = 120 / x t2 = 120 (x+10) Using t1 = t2 +1 we combine the two equations to This is solved by the following steps [rearranging terms] [multiply first term on right by (x+10) and second term on right by x to get a common denominator] [simplify and do subtraction] [simplify and rearrange] [simplify and rearrange] This is most easily solved by factoring. The factors are numbers that multiply to -1200 and add up to 10. Numbers that satisfy these criteria are 40 and -30. So the equation becomes which is true for x = -40 and x = 30. (why?) You cannot have a speed of -40. So x = 30. The speed of the first car is 30 miles/hr. The speed of the second car is 40 miles/hr. ****Checking gives: the first car travels for 120/30 = 4 hours. the second car travels for 120/40 = 3 hours.