{"subparts": [], "isOldForm": false, "hintString": " [string(latex(\\\\text{Distance} = \\\\text{Speed} \\\\times \\\\text{Time}).),string(If latex(ax^2 + bx + c = 0) then latex( x = \\\\frac{-b \\\\pm \\\\sqrt {b^2 - 4ac} }{2a }).),string(Put the value of latex(x) in the equation of speed.),string(Put the value of latex(x) in the equation of time.)]", "configString": " [name(\"\"\"BUS\"\"\",\"\"\"\"\"\"\"BUS\"\"\"\"\"\"\"),name(\"\"\"TRAIN\"\"\",\"\"\"\"\"\"\"TRAIN\"\"\"\"\"\"\"),name(X,\"X\"),name(Q,\"Q\"),two_speeds_with_relation(n,\"bus\",\"train\",x,40,\"less_than\"),two_times_with_var(n,\"bus\",\"train\",x,8,-437,4,-209),distance(n,q),config_text([\"string(A bus and a train travel the same distance at constant speeds. The speed of the bus was latex(x) km/h and the speed of the train was 40 km/h less than the speed of the bus. If the time taken by them were latex((8x - 437)) hours and latex((4x - 209)) hours respectively,)\"]),name(N,\"N\")]", "questionString": " [string(), string(A bus and a train travel the same distance at constant speeds. The speed of the bus was latex(x) km/h and the speed of the train was 40 km/h less than the speed of the bus. If the time taken by them were latex((8x - 437)) hours and latex((4x - 209)) hours respectively, find the distance travelled. )]", "solutionString": " [string(Speed of bus is latex(x) km/h and the speed of train is 40 km/h less than the speed of bus),string(latex(\\\\therefore) Speed of bus and train are latex((x)) km/h and latex((x - 40)) km/h and time taken by them are latex((8x - 437)) hours and latex((4x - 209)) hours respectively.),string(We know that, Distance = Speed x Time),string(latex(\\\\therefore) Speed of bus x Time taken by bus = Speed of train x Time taken by train),string(latex((x) \\\\times (8x - 437) = (x - 40) \\\\times (4x - 209))),string(latex(8x^2 - 437x = 4x^2 - 369x + 8360)),string(latex(\\\\therefore 4x^2 - 68x - 8360 = 0)),string(latex(4(x^2 - 17x - 2090) = 0)),string(latex(\\\\therefore x^2 - 17x - 2090 = 0)),string(Comparing latex(x^2 - 17x - 2090 = 0) with latex(ax^2 + bx + c = 0)),string(Thus, latex(a = 1, b = -17, c = -2090)),string(latex(\\\\therefore b^2 - 4ac = (-17)^2 - 4 \\\\times 1 \\\\times -2090 = 8649)),string(Now, latex(x = \\\\frac{-(-17) \\\\pm \\\\sqrt {8649} }{2 \\\\times 1}) latex(\\\\text{~~~~}) (Quadratic formula)),string(latex(x = \\\\frac{-(-17) - 93}{2 \\\\times 1} = -38) or latex(x = \\\\frac{-(-17) + 93}{2 \\\\times 1} = 55)),string(latex(\\\\therefore) latex(x = -38) or latex(x = 55)),string(When latex(x = -38)),string(Speed of bus latex( = x = -38 \\\\leq 0.) Hence, this speed is not possible.),string(Speed of train latex( = x - 40 = -38 - 40 = -78 \\\\leq 0.) Hence, this speed is not possible.),string(When latex(x = 55)),string(Speed of bus latex( = x = 55) km/h.),string(Speed of train latex( = x - 40 = 55 - 40 = 15) km/h.),string(When latex(x = -38)),string(Time taken by bus latex( = 8x - 437 = 8 \\\\times -38 - 437 = -741 \\\\leq 0.) Hence, this time is not possible.),string(Time taken by train latex( = 4x - 209 = 4 \\\\times -38 - 209 = -361 \\\\leq 0.) Hence, this time is not possible.),string(When latex(x = 55)),string(Time taken by bus latex( = 8x - 437 = 8 \\\\times 55 - 437 = 3) hours.),string(Time taken by train latex( = 4x - 209 = 4 \\\\times 55 - 209 = 11) hours.),string(Distance = Speed x Time),string(When speed = 55 km/h and time = 3 hours or speed = 15 km/h and time = 11 hours),string(Distance = latex(55 \\\\times 3 = 15 \\\\times 11 = 165) km),]", "answerTypeString": " [answer_types([[string(A),type(continuous(string(Distance = ),input(string(x),type(s_textbox)),string(km)))]])]", "must_get_html_from_browser": false}