SOLUTION: Hello. I seem to have particular trouble with word problems. I can't develop the equation so I never get to the point of solving it. Each time I do it correctly, it seems like a fl

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Travel -> SOLUTION: Hello. I seem to have particular trouble with word problems. I can't develop the equation so I never get to the point of solving it. Each time I do it correctly, it seems like a fl      Log On

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 Word Problems: Travel and Distance Solvers Lessons Answers archive Quiz In Depth

 Question 237530: Hello. I seem to have particular trouble with word problems. I can't develop the equation so I never get to the point of solving it. Each time I do it correctly, it seems like a fluke and I can't recreate it. I'd appreciate any help you can offer. Here is the question: Suppose that Car A can travel 250 miles in 3 hours less time than it takes Car B to travel 440 miles. The rate of Car B is 5 miles per hour faster than that of Car A. Find the rates of both cars. Found 2 solutions by scott8148, edjones:Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!time = distance / rate (250 / A) + 3 = 440 / (A + 5) multiplying by A(A + 5) ___ 250A + 1250 + 3A^2 + 15A = 440A 3A^2 - 175A + 1250 = 0 factoring ___ (3A - 25)(A - 50) = 0 3A - 25 = 0 ___ A = 25/3 ___ B = 40/3 A - 50 = 0 ___ A = 50 ___ B = 55 Answer by edjones(7569)   (Show Source): You can put this solution on YOUR website!You picked a tough problem but we can do it. a) what formula are you going to use? Ans.: st=d, speed * time=distance . b) speed Let s-5=car A's speed Let s=car B's speed . c)time Let t=car B's time . We can make a system of equations now. Look at the formula for B 1st because it is the simplest. A) (s-5)(t-3)=250 B) st=440 . B) s=440/t A) (440/t -5)(t-3)=250 Substitute 440/t for s (440-5t)(t-3)=250t multiply t times each side to eliminate the fraction. -5t^2+455t-1320=250t t^2-91t+264=-50t Divide each side by -5 t^2-41t+264=0 (t-8)(t-33)=0 Factor t=8 hrs, t=33 hrs If we use t=8 then for B: s=440/8=55mph Then for A: s=50mph . Check: A travels 250 mi in 5h B travels 440 mi in 8h which is 3hrs longer than A traveling 250mi. . Ed .